# Telescope optical tolerance from central axis

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I sometimes encounter telescopes/binoculars with a decent objective diameter but are very difficult to use because they only work when the eye is looking down the central axis (i.e. in the centre of the field) or close to it; if you try to focus on an object towards the edge of the field of view it goes black. Is there a name for this tolerance? It doesn't sound related to exit pupil but probably is something to do with eye relief - i.e. the distance of eye to the eyepiece lens.

## Quality Precision Optics

Numerous telescope designs exist for a wide variety of applications. Two basic families of designs emerge when described by the characteristics of their operation.

Afocal Systems: Incident light emerges collimated,
Focal Systems: Incident light is brought directly to a real image.

Within each family, various methods for producing desired results are possible, providing the potential user guidance in selecting an approach.

## How to understand OPD diagrams

Optical Path Difference (OPD) diagrams are the modern method of describing the performance of optical systems (especially regarding the colour correction of the optics).
Unfortunately, many manufacturers still publish &ldquoclassical&rdquo types of diagrams to describe their products. The most usual examples are spot diagrams and &ldquocolour curves&rdquo showing the focal length of different zones of the system. These diagrams are no longer optimal for modern optical systems.

When spot diagrams can still be used?

If a lens is corrected for off-axis lateral colour and off-axis coma (and this can be expected from any modern lens) and if the lens members are in one group (Petzval-like systems are excluded), then performance at the edge of the field is mostly independent from the actual design of the lens. No matter if the lens is air-spaced or oil-spaced, no matter if it is a doublet or a triplet, the performance will be (mostly) similar at the edge of the field, as long as the size/focal ratio is similar. For this reason, publishing off-axis diagrams for objective lenses is hardly justified, as what we would see in them are mostly off-axis astigmatism (native in systems where the members are in one group) and field curvature (also a native aberration).

Consequently, focal plane correctors (that correct both off-axis astigmatism and field curvature) are mostly universal devices, and only the focal length of the lens needs to be taken into account when choosing one. As in this case, off-axis performance mostly depends on the design and quality of the corrector, and for these correctors (and not for objective lenses) the publication of off-axis diagrams would be reasonable.

Furthermore, it is rather rare that a corrector would have diffraction-limited performance at the edge of the field, so, an APO lens with a field corrector is generally not a diffraction-limited system. Accordingly, the usage of spot diagrams is somewhat useful for showing the performance of a corrector (and most customers can easily interpret a spot diagram, as they have been commonly in use for many decades). Except for such cases, spot diagrams are not useful for modern APO telescopes.

How to interpret OPD diagrams

On the horizontal (&ldquoX&rdquo) axis of the OPD diagram, there is the diameter of the lens, i.e. left side of the X axis can be considered as left side of the lens.
On the vertical (&ldquoY&rdquo) axis of the diagram we can see the actual Optical Path Difference. This is usually measured in &ldquolambda&rdquo, i.e. the wavelength of light. Differently coloured curves usually mean different wavelengths.

If a lens is theoretically perfect in a given colour (e.g. our aspheric figured lenses in green colour wavelength) then diagram corresponding to this colour is a straight horizontal line that doesn&rsquot deviate from the &ldquo0&rdquo value in the Y direction, meaning that the curve runs flat along X axis.

If a colour is defocused, then its curve will be &ldquoU&rdquo shaped or an inverted &ldquoU&rdquo, depending on the direction of de-focus.
If a lens has spherical aberration in a given colour, then curve of this colour will show an &ldquom&rdquo shape or an inverted &ldquom&rdquo, depending whether there is spherical under &ndash or over-correction.

### FIG.3 - VIOLET CORRECTION

The modern definition of apochromatism sets minimum values of Strehl ratios in different colours, as it&rsquos performance requirements for colour correction. The Strehl ratio cannot be directly seen in the OPD diagrams, but, as modern lenses (mostly) have spherical errors in blue/red colours and &ldquoclean&rdquo spherical aberration can easily be converted into Strehl values, a good approximation is to check the OPD diagrams for these parameters:

&ndash the blue OPD diagram should &ldquostay&rdquo within a 1/4 lambda vertical &ldquorange&rdquo
&ndash the red OPD diagram should &ldquostay&rdquo within a 1/4 lambda vertical &ldquorange&rdquo
&ndash the violet OPD diagram should &ldquostay&rdquo within a 1/2 lambda vertical &ldquorange&rdquo

Fulfilling these requirements does not (yet) mathematically prove that the given lens matches the APO definition. The Strehl values need to be verified in order to do so, but they can be easily estimated by simply looking at the diagrams. Matching these requirements already proves that the lens is minimally close to matching the APO definition. In other words: the difference of such a lens from a &ldquoproven APO&rdquo is mostly theoretical.

For the sake of making this easier to understand, we marked the lowest part of the blue OPD diagram of an 80mm lens in the Fig.2 . The lower blue line is placed at the lowest part of the blue diagram (in the middle of the lens) and the top blue line is drawn at 0,25 lambdas above the first. As the actual blue OPD diagram of the lens very easily fits between these limits (in fact it stretches vertically to only about half the limit), the lens looks like a highly colour- corrected lens that has parameters significantly exceeding the requirements of the APO definition. The Strehl calculation shows about 94% Strehl for this lens, both in red and blue colours (this is well above the required 80% limit), in conclusion the lens is really a highly corrected APO.

If we check the performance of the same lens in violet colour (Fig.3), then we might note that the performance is still better than the 1/2 lambda limit, but the deviations in this colour approach 80% of the allowed limit, unlike the roughly 50% we have seen in blue colour. This is natural for such fast (F/6) lenses but fortunately the lens seems to be a real APO even in violet. As the Strehl calculation shows about 58% Strehl, this &ldquoquick check&rdquo method seems to be working again.

The OPD diagrams we publish are based on a given melt of actual optical glass, i.e. on the measured glass parameters we received from the glass melting company. Some other manufacturers publish diagrams based on glass catalogue values, which is also a viable approach. But there is a caveat concerning every lens manufacturer:

The variations of glass from melt to melt are actually of a much larger magnitude than &ldquoby design&rdquo optical errors of modern lenses. In other words, every batch of lenses (built from a consequent melt of glass) must be &ldquotuned&rdquo to match the optical parameters of the actually used glasses. This necessitates effort, the creation of additional tools and time. Some manufacturers prefer to save money and time by not tuning colour correction of the lenses, using &ldquogeneric&rdquo tools and hoping that colour correction will still be acceptable , which does occur in most cases. These lenses will show different colour correction from batch to batch. This might be acceptable for cheaper APOs using less advanced glasses (with lenses that won&rsquot match the APO definition anyway, but if we want to have really colour free images, then we do not only have to look at theoretical performance or glass recipe, but we should also check how tightly the manufacturer can measure and control colour aberrations. Building multi-colour interferometers has become more feasible in recent times, but a manufacturer without such a device could hardly provide lenses with identical colour correction.

Pal Gyulai
Optical Designer of refractive optics
CFF Telescopes

## COMPREHENSIVE TELESCOPES DESIGNS GUIDE

The types of telescopes are basically 3, refractors, reflectors, and compound telescopes. Refractor telescopes are comprised by lenses, reflectors have mirrors and compound have both. There is no optical design that is perfect, so each design is more suitable for the specific astronomical subjects that are going to be observed, photographed, or studied.

Glossary of terms used to describe a telescope optical features and capabilities:

Size of the telescope’s objective generally referenced by its diameter’s length. A bigger aperture will provide a greater light gathering capability and higher resolution.

Bigger Aperture = better visibility of smaller and fainter details

Focal length

Distance between the objective and the focal plane where the concentrated light rays converge projecting a focused image. The focal length alters the magnification and the field of view of a telescope.

Shorter focal length = wider field of view and lower magnification

Longer focal length = narrower field of view and higher magnification

Focal ratio

Is the proportional relation between the focal length and the aperture of a telescope. Calculated dividing the focal length by the diameter of the objective. The resulting number determines the photographic speed. The higher the number the slower, and the lower the number the faster. Also known as “f/number” or “f/stop”

To collect the same amount of detail in photography:

Lower f/number = Shorter exposure

Higher f/number = Longer exposure

The focal length of a telescope can be modified with a focal reducer to shorten it, and a focal extender or barlow to enlarge it. By reducing the focal length, it will also change the focal ratio to a lower number. Increasing the focal length will also raise the focal ratio number.

On-Axis: The exact center of the field of view.

Off-Axis: out of the center of the field of view.

Diffraction-limited optics

Image quality is mainly affected by the original wave properties of light and the residual wave error induced by the optics aberrations is one-quarter of wavelength of light or smaller.

Optical aberrations

Are figure imperfections on the optics that distort the original wave patterns of incoming light to the objective. The most common are spherical aberration and astigmatism.

Spherical Aberration

In this aberration the converging light rays from the center and out the center of the objective do not focus at the same distance over the center line (optical axis) of the focal plane, resulting in multi-focal points distances between the objective and the focal plane along the optical axis blurring the projected image.

Astigmatism

When the lens or mirror is not perfectly round with a figure tending toward an oval shape that is not rotationally symmetrical, it makes the stars appear to have a “cross like” shape. Astigmatism aberration impacts the image sharpness.

Spherical and astigmatism aberrations affect the entire image field, from the exact center to the very edge.

Field curvature

Is the natural spherical curve produced by the projected beam of light due to the optical surface geometry of the lens or mirrors. In prime focus to an image sensor, the light rays projected from out of the center of the objective (off-axis) will come into focus before reaching the sensor’s surface. This is not an issue when the focal plane is a curved or spherical surface, such as the human eye. For this reason, field-flattener corrector lenses are used in astrophotography to produce flat-field images.

Astrograph: Telescope design optimized or dedicated for astrophotography.

Telescope’s usage purpose

For observations of bright objects such as planets or the moon, whether from an area with light pollution or without pollution, a refractor telescope with 3” to 4” inches of aperture’s diameter or a reflector or compound telescope of 4.5” to 6” inches of aperture is more than enough for observing planets, the moon, double stars, or open stars clusters.

The observation of bright objects such as Jupiter, Saturn or the Moon, is not affected at all by the pollution produced by streetlights in cities with dense population. Short focal length refractors and small Newtonian telescopes have a wide field of view suitable for bright deep space objects observations at low magnifications.

For faint deep sky objects observations, Newtonian reflectors, or compound telescopes with apertures of 8” inches and bigger are recommended, especially when used in locations with little or no light pollution. These last-mentioned telescopes with big apertures also offer spectacular and highly detailed views of the planets and the moon.

Regarding astrophotography, apochromatic refractors are usually one of the best choices for wide field imaging of the night sky. Schmidt-Cassegrains and other Cassegrain variants telescopes are suited for deep field imaging of distant galaxies, nebulae, and planetary astrophotography as well. Some apochromatic refractors with Petzval optical design like Takahashi FSQ-106 and the Corrected Dall-Kirkham telescopes produce a large corrected flat-field image circle that can illuminate completely a medium format sensor without vignetting. Ritchey-Chretien telescopes are the most suited for scientific astronomical research.

Lens elements on refractors telescopes are commonly made of borosilicate glass. Mirrors on reflectors and compound telescopes are made of borosilicate, soda lime or pyrex glass with an aluminum layer as the reflective material covered by silicon dioxide for its protection and durability.

Carbon fiber optical tubes have a reduced thermal contraction/expansion with temperature variations minimizing focal point position changes.

The most common telescopes designs commercially available today are described in depth below.

Achromatic refractor

The achromatic refractor telescope has two glass or lens elements called crown and flint, that refracts or bends the light converging its rays to project an image at a focal plane, enlarging or magnifying any object’s size visually like a magnifying glass for reading or crafting will do. Refractor telescopes are the best known historically since Galileo Galilei used the single element refractor for his study of the moon, the planet Jupiter, and solar observations. They are commercially available from 50mm diameter to 150mm (2.4 to 6 inches). A refractor telescope is the icon of what most people know as a telescope and what it should look like. They have good a correction for chromatic aberration in telescopes with focal ratio from f/12 to f/15. This aberration consists of blue/purple light wavelength not converging at the same focal plane as red and green light wavelengths resulting in blue hues out of focus noticeable around bright objects like the Moon, Jupiter, Venus and bright stars. Known brand names makers of achromat refractors are Explore Scientific, Celestron, Meade, Vixen and Orion. They are available in apertures from 50mm to 150mm (2” to 6”)

Apochromatic refractor

They offer significantly better correction of chromatic aberration than achromatic refractors due to an extra-low dispersion glass element, traditionally composed of calcium fluoride, known as “fluorite”. The substantial color correction is done by reducing the difference in refractive index of blue wavelength spectrum related to red and green wavelength spectrums focusing on the same focal plane. Blue or purple halos on bright objects such as the moon or planets are not noticeable even in telescopes with medium or fast focal ratio (f/5 to f/7). They can have 2 elements (doublet) or 3 elements (triplet) the best apochromatic telescopes typically have three elements with one extra-low dispersion glass element sandwiched between the other two glass elements. Known apochromatic refractors manufacturers are Explore Scientific, Meade, Stellarvue, Sky-Watcher, Takahashi, William Optics, etc. Typically available in apertures from 50mm to 165mm. (2” to 6.5”)

Apochromatic refractors deliver the best quality views with the highest contrast than any other telescope design.

Petzval Refractor design

Is a quadruplet refractor astrograph with two front elements group and two rear elements group. When one or two of the optical elements is made of fluorite or ED glass, the overall color correction achieves full apochromatic performance. It is highly corrected to reduce spherical and astigmatism aberrations with a fast focal ratio (typically around f/5) producing a large image circle with flattened field curvature. The Takahashi FSQ-106 is the most known top-notch fast refractor astrograph with this optical design. The William Optics Red Cat has also the Petzval lens configuration.

Solar Refractor Telescope

Solar refractor telescopes are achromatic refractors dedicated to observe and photograph the sun, which may have one or two etalon solar filters built into the optical tube, one in front of the objective and one before the focal plane. Etalon is a filter made of one or two flat crystals with 2 reflective surfaces that deflect a significant percentage of the light spectrum. They are designed to isolate and transmit a narrow bandwidth corresponding to a specific wavelength for the emission of hydrogen alpha. With this telescope is possible to see sunspots, prominences, filaments, granulations and flares. They are mainly made by Meade Coronado, Lunt and DayStar brands.

• Unobstructed light path for higher contrast views than reflectors and compound telescopes
• Round stars with no diffraction spikes compared to Newtonians or other Cassegrain reflectors
• Best telescope design for lunar, planetary and double star observations
• Well-suited for terrestrial observations as a spotting scope
• Apochromatic refractors deliver the best quality views with the highest contrast
• Excellent for wide field observations and astrophotography
• Practically never will require optics collimation (on collimatable models only) if the optical tube has been severely dropped or bumped
• Dedicated reducers or field flatteners are usually available from the same telescope’s manufacturer or 3 rd party brands. Generally suitable for full frame imaging sensors.
• Refractors’ lenses do not require recoating like reflectors’ mirrors usually do after 10 years
• No mirror shift/flop issues
• Better choice than Newtonian telescopes for large color cameras or monochrome imaging with filter wheels because the focuser is installed on the rear end of the optical tube with better balance
• Highest cost per inch of aperture among all telescope’s designs
• Due to the most expensive optics design and difficulty to manufacture, refractors are limited in apertures usually up to 6 inches
• Because the aperture limitation, are less appropriate for faint deep sky objects observations like far away galaxies and nebulae
• Longer and heavier optical tubes than Newtonians and Schmidt-Cassegrain telescopes of the same aperture size
• Dew is prone to form over the objective lens in humid environments. Heaters might be required to reduce or eliminate condensation
• Tube current issues on significant temperature changes with bigger apertures. Takes longer to reach thermal equilibrium (cool down) than newtonian telescopes or other open tube reflectors due to the closed tube design
• Uncomfortable low level eyepiece viewing position when pointing straight up with long focal length refractors
• With focal lengths longer than 1000mm, the optical tube might require a tripod pier extension to avoid movements range limitation with tripod legs
• Solar dedicated refractors telescopes can be used only to see and photograph the sun
• Short tube refractors might require risers blocks to avoid the camera or imaging train obstruction with the optical tube dovetail

Newtonian reflector

Invented by Sir Isaac Newton in 1668, the Father of the theory of gravity and celestial mechanics, it consists of a concave (shaped inwards) primary mirror of spherical or parabolic figure that reflects the light magnifying, enlarging or “Zooming in” the image like those magnifying mirrors that women use for face cleansing and make up. The light rays reflected from the primary mirror converge at a focal plane projecting an image through the reflection of another flat secondary mirror placed in the path of light being held by 3 or 4 spider vanes structure. This secondary mirror directs the light at a 90 ° angle towards the focusing tube where an eyepiece for observation or camera for astrophotography is attached. Available between 3 to 12 inches in aperture’s diameter (76mm to 305mm) to be used with Alt-Az mounts (small apertures) and equatorial mounts (up to 12” f/4 astrographs). Newtonian telescopes with Dobsonian mounts are commercially between 4.5 to 25 inches in aperture’s diameter (114mm to 635mm). Common brand names of Newtonian telescopes are Celestron, Meade, Orion and Sky-Watcher.

• The best bang for the buck with the lowest cost per inch of aperture
• Significantly better for faint deep sky objects observations than refractors telescopes because the bigger apertures availability
• Absent color aberration (Zero Chromatic aberration without relay lens or correctors)
• Somewhat Shorter optical tube than refractors telescopes
• Faster cool down with open optical tube design compared to refractors and compound telescopes
• Significantly reduced dew issues because there are no glass elements at the optical tube opening
• Wider field of view than Schmidt-Cassegrain and other Cassegrain variant telescopes
• With usually fast focal ratios (f/4 to f/6) a focal reducer is not necessary to shorten exposures’ length for deep sky astrophotography
• F/4 imaging Newtonians are the best value for astrophotography. With a coma corrector are suitable for full frame imaging sensors
• Being fast telescopes, are also an excellent value for EAA (Video Astronomy)
• Reduced mirror shift compared to Schmidt-Cassegrain and Maksutov-Cassegrain telescopes because the primary mirror is fixed to the rear cell of the optical tube
• Available in carbon fiber truss tubes open optical tube structure, for even faster cool down and reduced thermal contraction/expansion with temperature variations minimizing focal plane position changes
• Contrast reduction due to the objective’s central obstruction caused by the secondary mirror
• Diffraction spikes effect visible on stars caused by the secondary mirror spider vanes structure
• Newtonian telescopes require frequent collimation of the mirrors if they are often transported to dark skies observing locations. When shipped, most of the time arrives with the mirrors out of collimation.
• Subject to coma aberration where stars out of the center towards the edge of the field of view have a “comet like” shape. This aberration is more noticeable with f/6 and faster focal ratios
• Usually not suitable for terrestrial observations due to the inverted upside down and backwards image
• Uncomfortable low level eyepiece viewing position when pointing lower towards the horizon with dobsonian mounts
• Newtonian telescopes bigger than 12” or 16” inch of aperture will require a ladder to observe through the eyepiece when pointing straight up
• Significantly longer optical tubes than Schmidt-Cassegrain and other Cassegrain variant telescopes.
• Open optical tube design exposes the mirrors to dust and moisture
• Reflectivity ratio reduced after 10 years. Eventually after that time might require mirrors recoating service.
• Requires a coma corrector for a flat field image circle in deep sky astrophotography
• 3X to 5X focal extender required for planetary imaging
• Optical tube unbalance issues when imaging with a large camera or long imaging trains. May require additional counterweights for the optical tube to properly balance the mount’s Declination axis

Maksutov-Newtonian

This telescope is basically a Newtonian reflector, incorporating the concave maksutov corrector lens which holds the secondary mirror. It typically has a fast f/5 focal ratio and offers a wide, substantially corrected field of view and delivers high contrast in planetary and double star observations quite similar to an apochromatic refractor telescope. For Astrophotography, a coma corrector is not mandatory to flatten the image circle because the Maksutov corrector lens already reduces coma and spherical aberrations. Due to the manufacture difficulty of the Maksutov corrector lens, Maksutov-Newtonians are generally available only in 6 or 7.5 inches (150mm or 190mm) of aperture diameter from Sky-Watcher, Explore Scientific and Orion.

• Mimics the apochromatic refractor views with excellent contrast on lunar and planetary observations for a fraction of the cost
• Corrected wide rich-field ideal for observations of large deep space objects and open star clusters
• Reduced spherical and coma aberrations. No coma corrector needed for deep space astrophotography
• Like refractors, stars look round with no diffraction spikes compared to Newtonians or other Cassegrain reflectors telescopes
• Closed tube design protects the telescope’s mirrors against dust and moisture
• Maksutov-Newtonian telescopes are limited in apertures availability up to 7.5 inches
• More expensive than Newtonian telescopes
• Dew is prone to form over the corrector lens in humid environments. Dew shield and heaters are required to reduce or eliminate condensation
• Tube current issues on significant temperature changes. Takes longer to reach thermal equilibrium (cool down) than newtonian telescopes or other open tube reflectors due to the closed tube design

Cassegrain based telescopes designs

The original Cassegrain reflector design was attributed to Laurent Cassegrain of France in year 1672. The Cassegrain based telescopes design have a concave (shaped inwards) primary mirror (that “Zooms in” or magnify the image) converging the light rays with a focal ratio of f/2 to f/2.5 and a convex (shaped outwards) secondary mirror with a focal ratio of f/4 to f/5. The secondary mirror “zooms out” the image diverging the light rays to increase the telescope’s effective focal length just like cars’ side mirrors with the “Objects in mirror are closer than they appear” warning do. Both primary and secondary mirrors are squared facing each other frontally. The secondary mirror reflects the concentrated light from the primary mirror perpendicularly through a hole in the same primary mirror and the focal plane is behind of it.

• Very compact optical tube due to the “folded” light path reflection design
• Having a long focal length are excellent for lunar, planetary and double stars observations and astrophotography with large angular size
• Well suited for deep field observations and astrophotography of small faint objects like distant galaxies and nebulae because the big apertures availability and the long focal length
• Lower cost per inch of aperture than refractor telescopes
• Comfortable eyepiece level observing position when pointing at any direction (straight-up or towards the horizon)
• Better choice than Newtonian telescopes for imaging with large color cameras or monochrome cameras with filter wheels because the focuser is installed on the rear end of the optical tube with better balance
• Contrast reduction due to the objective’s central obstruction caused by the secondary mirror
• Narrower field of view than Newtonians and refractors telescopes because the longer focal length
• With generally slow focal ratios, a focal reducer is required to shorten the astrophotography exposures’ length
• Higher cost per inch of aperture than Newtonian telescopes because the secondary curved mirror is more difficult to figure than a flat mirror
• Might require occasional or frequent collimation of the mirrors if they are often transported to dark skies observing locations
• Reflectivity ratio reduced after 10 years. Eventually after that time might require mirrors recoating service.

Schmidt-Cassegrain

They are comprised by a corrector plate and mirrors. The most popular compound telescopes are the Schmidt-Cassegrain design, a variant of the Cassegrain reflector telescope with a Schmidt corrector plate. They generally have a spherical or parabolic primary mirror and a spherical secondary mirror. The corrector plate has an aspherical figure and also holds the secondary mirror. The focal ratio of a Schmidt-Cassegrain telescope is typically f/10, and its corrector plate reduces spherical aberration in green light, which is the most noticeable wavelength spectrum for the human eyes’ sensitivity. These telescopes are typically available from 5 to 14 inches apertures from Celestron and Meade brands.

• Most versatile design as 3 in 1 telescope with Hyperstar (f/2) for widefield astrophotography, f/6.3-f/7 for deep space observations and astrophotography and f/10 for terrestrial, planetary/deep space observations and astrophotography
• More accessories available for observations and astrophotography than any other telescope design
• Like refractors, stars look round with no diffraction spikes compared to Newtonian or other Cassegrain reflectors telescopes
• Higher-end models have built-in correctors for a flat coma-free field of view suitable for full frame sensors
• Dedicated reducers are available from the same telescope’s manufacturer
• Closed tube design protects the telescope’s mirrors against dust and moisture
• Mirror shift or flop because focus is achieved by moving the primary mirror
• Dew is prone to form over the corrector plate glass in humid environments. Dew shield and heaters are required to reduce or eliminate condensation
• Tube current issues on significant temperature changes. Takes longer to reach thermal equilibrium (cool down) than newtonian telescopes or other open tube reflectors due to the closed tube design
• Standard Schmidt-Cassegrains exhibit coma aberration on prime focus imaging and the projected image circle is not suitable for full frame sensor cameras

Maksutov-Cassegrain

Another variant of the Cassegrain reflector is the Maksutov-Cassegrain. It incorporates the concave, negative figured spherical corrector plate that corrects spherical and coma aberrations, and its focal ratio is typically f/12 or f/15. In the Maksutov-Cassegrain telescope, the secondary convex mirror is just an aluminized spot in the center of the corrector plate. The Maksutov corrector plate is difficult to manufacture in big sizes. These telescopes are available typically from 3.5 to 7 inches apertures.

• Most compact optical tube among all telescope designs. Best for backpack portability.
• Well-suited for terrestrial observations as a spotting scope
• Like refractors, stars look round with no diffraction spikes compared to Newtonian or other Cassegrain reflectors telescopes without a corrector plate
• Are mostly collimation-free with the optics elements aligned at the factory
• Closed tube design protects the telescope’s mirrors against dust and moisture
• Maksutov-Cassegrain telescopes are limited in apertures availability up to 7 inches
• Mirror shift or flop because focus is achieved by moving the primary mirror
• Dew is prone to form over the corrector lens in humid environments. Dew shield and heaters are required to reduce or eliminate condensation
• Tube current issues on significant temperature changes. Takes longer to reach thermal equilibrium (cool down) than newtonian telescopes or other open tube reflectors due to the closed tube design
• Slower native focal ratio than Schmidt-Cassegrain telescopes
• No dedicated reducers available from the same telescope’s manufacturer
• The projected image circle at prime focus is not suitable for full frame sensor cameras

Ritchey-Chretien Telescope

It was developed by astronomers George Willis Ritchey and Henri Chrétien in the early 1910s. This design is a variant of the Cassegrain reflector telescope with both primary and secondary hyperbolic mirrors with usually f/8 or f/9 native focal ratios. It is highly corrected for spherical aberration and coma. The Ritchey–Chrétien telescope is the most chosen optical design by professional observatories for astronomical scientific research. The Hubble and Spitzer Space telescopes are configured with the Ritchey-Chretien optical design. Commercially available in apertures from 6-inch to 24-inch.

• Excellent Astrophotography performance with a coma-free field of view appropriate for full frame sensor cameras
• Suitable for Astrometry, photometry and spectroscopy
• Faster native focal ratio than typical f/10 Schmidt-Cassegrain telescope
• Zero chromatic aberration without any refractive element like reducer/corrector lenses
• Most accurate reading from ultraviolet to infrared light wavelength’s spectrum research on a pure mirror to monochrome sensor imaging configuration
• Increased infrared sensitivity on Ritchey-Chretien telescopes’ mirrors with golden coatings
• Significantly reduced dew issues because there are no glass elements at the optical tube opening
• Reduced mirror shift compared to Schmidt-Cassegrain and Maksutov-Cassegrain telescopes because the primary mirror is fixed to the rear cell of the optical tube
• Faster cool down with open optical tube design compared to refractors and compound telescopes
• Available in carbon fiber truss tubes open optical tube structure, for even faster cool down and reduced thermal contraction/expansion with temperature variations minimizing focal plane position changes.
• Less suitable for observations due to the large central obstruction (over 45% by diameter)
• Heavier than Schmidt-Cassegrain telescopes because the larger secondary mirror size and support structure. Also, the external focuser sums additional weight.
• Demands perfect or near perfect collimation. A slight misalignment of the mirrors will cause a significant impact in the optical performance because the tight tolerance of the secondary mirror optical axis
• Diffraction spikes effect visible on stars caused by the secondary mirror spider vanes structure
• Field curvature of image circle is not flattened because the lack of built-in field flattener lens
• No dedicated reducers or field flatteners available from the same telescope’s manufacturer
• Open optical tube design exposes the mirrors to dust and moisture

Corrected Dall-Kirkham (CDK) Telescope

The CDK telescope has an elliptical primary mirror, a spherical secondary mirror, and corrector lens group near the focal plane. This optical design configuration delivers an image free of coma and off-axis astigmatism with a flat field. The corrected field is considerably larger than the Ritchey-Chretien telescope without a corrector lens. Native focal ratio is usually over f/7 to f/8. Known telescopes with this optical design are Hubble Optics CDK, Planewave and Takahashi Mewlon. Available in apertures from 10-inch to 1 meter.

## Telescope optical tolerance from central axis - Astronomy

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Optical design of diffractive telescope system based on off-axis three mirror

Chuanwang He, 1,2 Peng Huang, 1,2 Xiaochun Dong, 1 Bin Fan 1

1 Institute of Optics and Electronics (China)
2 Univ. of Chinese Academy of Sciences (China)

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Diffractive telescope has the advantages of lightweight and loose tolerance, so it can become the next generation space telescope. In order to realize no central obscuration, compact structure and large field of view (FOV), the off-axis three mirror is used as eyepiece in diffractive telescope system. According to the Schupmann’s achromatic theory, an optical design example of diffractive telescope with 0.8m aperture of objective lens, 0.46

0.54&mum spectral bandwidth and 0.08° FOV is presented. By using the function of coordinate break in optical design software ZEMAX, an unobscured diffractive telescope system based on off-axis three mirror eyepiece is realized. After optimized original structure parameters, the diffractive telescope system has a good performance with 39.1m short total length. Here, at the spatial frequency of 50lp/mm, the values of modulation transfer function (MTF) within full FOV are greater than 0.574. Furthermore, the values of RMS radius are less than airy radius diameter. The optimized results clearly show that the system is achromatic and near diffraction limited imaging quality.

## PlaneWave 24-inch F/6.5 CDK with Fused Silica Mirrors and Delta-T Heaters

Created to meet the demands of both the serious imager and visual observer, the PlaneWave CDK is a revolutionary new telescope optical system invented by Dave Rowe. Offered at an unprecedented value for a telescope of this quality and aperture, the goal of the design was to make an affordable astrographic telescope with a large enough imaging plane to take advantage of the large format CCD cameras of today. The CDK design far exceeds the off-axis performance of most commercial telescope designs, including the Ritchey Chretien.

The RMS spot sizes at the edge of a 35mm frame remain smaller than a single pixel on the most advanced CCD cameras available to amateurs today. Most telescope images degrade as you move off-axis from either coma, off-axis astigmatism, or field curvature. The CDK design suffers from none of these problems.

The CDK is coma-free, has no off-axis astigmatism, and has a flat field. The design is a simple and elegant solution to the problems posed above. The CDK consists of three components: an ellipsoidal primary mirror, a spherical secondary mirror, and a lens group. All these components are optimized to work in concert in order to create superb pinpoint stars across the entire 70mm image plane.

One of the unique features of the CDK design is its ease of collimation and achievable centering tolerance for a telescope of its class. This ease of alignment and collimation guarantees the user will be sure to get the best performance out of the telescope possible, each and every night. The end result at the image plane of the CDK design is pinpoint stars from the center of the field of view out to the corner of the field of view.

### Comparison: CDK vs Ritchey Chretien

The Ritchey design was popularized as an astro-imaging telescope due to its use in many professional observatories. Although very difficult and expensive to manufacture and align, the Ritchey is successful in eliminating many of the problems that plague many other designs, namely off-axis coma. However, the Ritchey does nothing to eliminate the damaging effects of off-axis astigmatism and field curvature.

The CDK design tackles the off-axis coma problem by integrating a pair of correcting lenses into a two-mirror design. The beauty is that this design also corrects for astigmatism and field curvature. Because the lenses are relatively close to the focal plane (unlike the Schmidt corrector plate found in various Schmidt-Cassegrain designs), and because these lenses work together as a doublet, there is no chromatic aberration. The CDK offers a wide aberration-free, flat field of view that allows the user to take full advantage of the very large imaging chip cameras in the marketplace today.

Having an aberration free telescope design means nothing if the optics cannot be aligned properly. Many Ritchey owners never get to take full advantage of their instrument's performance because the Ritchey is very difficult to collimate. Aligning the hyperbolic secondary mirror's optical axis to the optical axis of the primary mirror is critical in the Ritchey design, and the tolerances are unforgiving. The secondary mirror of the CDK design is spherical. It has no optical axis and so the centering tolerance of the CDK secondary mirror is comparatively huge. With the help of some very simple tools, the CDK user will be able to set the secondary spacing, collimate the optics and begin enjoying the full performance potential the instrument has to offer within a few minutes.

In the comparison shown above the drastic difference in performance between the CDK and the RC is apparent. The biggest component that degrades the off-axis performance of the RC is the defocus due to field curvature. In many diagrams shown by RC manufacturers, the diagrams look better than this because they are showing a curved field. This is fine for visual use because the eye can compensate for some amount of curvature of field. But CCD arrays are flat and so in order to evaluate the performance a spot diagrams and/or diffraction simulations requires a flat field.

## Telescope optical tolerance from central axis - Astronomy

Thermal Conductivity, W/(m K)

Q: How can I be sure RCOS optics are excellent?
A: Each RCOS telescope is supplied with an interferogram and wavefront analysis which objectively describe the precision of each optical set. The optical sets are made by Star Instruments (USA) who also supply professional observatory optics to manufacturers such as DFM Engineering and Optical Guidence Systems Inc. We certify each and every optical set. Many mass production manufacturers simply do not supply ANY data, and simply rely on their legal and advertising departments.

Q: What about advantages of the RC design from a visual, CCD and photographic perspective?
A: The Ritchey-Chretien was originally designed specifically as a photographic instrument. Its wide coma free field is advantageous for any application. Especially with medium format film and high-resolution large array CCD cameras. Visually the image is rather like a refractor, with pin point stars to the edge of the field. Despite the large secondary obstruction, planetary images are very crisp, due to the excellent figure and polish of all RCOS optics.

Q: Why use a secondary focuser?
A: Most SCT's achieve focus by moving their primary mirrors. While this does allow a massive range of focus, it also imparts mirror flop and field shift as the telescope is moved or focused. The secondary focuser in all RCOS telescopes uses extremely high precision bearings to impart zero image shift over a similarly wide focus range. As the primary is rigidly held in place there is no mirror flop or field shift.

Q: Can I use an F/6.3 or a F/3.3 reducer?
A: We recommend the Astro Physics .75X telecompressor. Other brands of focal reducer (e.g. Celestron and Meade) will cause modest vignetting which can be removed by an accurate CCD flat frame, but would be difficult to remove from a photographic image.

Q: Does it use baffles?
A: The primary and secondary mirrors are both baffled. The primary baffle has internal light stops.

Q: Are the optics coated?
A: Since coatings and applications can be varied, its your choice on what type of coatings and which company to use. If requested, we'll be happy to make suggestions.

Q: Why are cooling fans necessary?
A: Heat build up in any set of optics will cause thermal air currents which can severely distort the image seen through the telescope. RCOS telescopes have cooling fans which gently draw ambient air through the telescope to negate any thermal air current effects.

Q: Why use a Carbon Fibre tube assembly?
A: Carbon fibre has excellent thermal and strength for weight properties that make it an ideal material for telescope tube assemblies. The carbon tube has significantly less thermal expansion and contraction than an aluminium tube, yet weighs a fraction of a similarly rigid metal or sonotube (i.e. cardboard) assembly. As a result the telescope will not sag or lose alignment under different orientations or shift focus as the temperature changes during a night's observing.

Note : some SCT manufacturers are now using carbon fibre outer tubes, but still fully mount and move their mirrors along an aluminium baffle tube, totally negating any benefits of a carbon composite tube assembly.

Pricing:
The smallest telescope in the RCOS range (250mm) costs about double that of a 14" Schmidt Cassegrainian (about $A25,000) A 12.5" RCOS telescope complete with a robotic German equatorial mount is priced similarly to competing 16" SCT's ($A43,000), yet offers vastly superior optics, instrument tracking, pointing, and stability.

Exact prices however, are quoted on a per instrument basis, and will vary with the $A to$US at the time of ordering.

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## The CDK Optical Design

The CDK [Corrected Dall-Kirkham] telescope is based on a new optical design developed by Dave Rowe. The goal of the design is to make an affordable astrographic telescope with a large enough imaging plane to take advantage of the large format CCD cameras of today. Most telescope images degrade as you move off-axis from either coma, off-axis astigmatism, or field curvature. The CDK design suffers from none of these problems. The end result is a telescope which is free from off-axis coma, off-axis astigmatism, and curvature of field, yielding a perfectly flat field all the way out to the edge of a 52mm image circle. This means pinpoint stars
from the center out to the corner of the field of view.

The design is a simple and elegant solution to the problems posed above. The CDK consists of three components:

All these components are optimized to work in concert in order to create superb pinpoint stars across the entire 52 to 70mm image plane.

#### Optical Performance

At this point, we will show you two diagrams, to convince you about the high image quality of the CDK20. The first is a diffraction simulation and the second is a spot diagram. In the diffraction simulation the star images on axis and off-axis are nearly identical. In the
spot diagram 21mm off-axis the spot size is an incredible 6 microns RMS diameter. For 26mm off-axis, a 52mm image circle, the RMS spot size is 11 microns. This means the stars across the entire focal plane are going to be pinpoints as small as atmospheric seeing
will allow. Both of the simulations take into consideration a flat field, which is a more accurate representation of how the optics would perform on a flat CCD camera chip.

For visual use some amount of field curvature would be allowed since the eye is able to compensate for a curved field. The diffraction simulation was calculated at 585nm. The spot diagram was calculated at 720, 585, and 430nm. Many companies show spot diagrams in
only one wavelength, however to evaluate chromatic performance multiple wavelengths are required.

NGC 6992 – PlaneWave CDK14 – Nikon D810A – 1x480s – 36,3 MP – UNGUIDED (0,38 arcsec)

#### Comparison: CDK vs. Ritchey Chrétien

The simulations shown compares the optical performance of the CDK design to the Ritchey Chrétien (RC) design. The Ritchey design was popularized as an astroimaging telescope due to its use in many professional observatories. Although very difficult and expensive to manufacture and align, the Ritchey is successful in eliminating many of the problems that plague many other designs, namely off-axis coma. However the Ritchey does nothing to eliminate the damaging effects of off-axis astigmatism and field curvature.

The CDK design tackles the off-axis coma problem by integrating a pair of correcting lenses into a two mirror design. The beauty is that this design also corrects for astigmatism and field curvature. Because the lenses are relatively close to the focal plane, and because these lenses work together as a doublet, there is no chromatic aberration. The CDK offers a wide aberration-free, flat field of view that allows the user to take full advantage of the very large imaging chip cameras in the market place today.

Having an aberration free telescope design means nothing if the optics cannot be aligned properly. Many Ritchey owners never get to take full advantage of their instrument’s performance because the Ritchey is very difficult to collimate. Aligning the hyperbolic secondary mirror’s optical axis to the optical axis of the primary mirror is critical in the Ritchey design, and the tolerances are unforgiving. The secondary mirror of the CDK design is spherical. It has no optical axis and so the centering tolerance of the CDK secondary mirror is comparatively huge. With the help of some very simple tools, the CDK user will be able to set the secondary spacing, collimate the optics and begin enjoying the full performance potential the instrument has to offer within a few minutes.

The drastic difference in performance between the CDK and the RC is apparent. The biggest component that degrades the off-axis performance of the RC is the defocus due to field curvature. In many diagrams shown by RC manufacturers, the diagrams look better than this because they are showing a curved field. This is fine for visual use because the eye can compensate for some amount of curvature of field. But CCD arrays are flat and so in order to evaluate the performance a spot diagrams and/or diffraction simulations requires a flat field as shown.

The small squares are 9x9 microns wide, the individual comparative images are 90 micrometers wide. The spot diagrams were calculated for a wavelength of 585 nanometers.

Furthermore, please note: the CDK design is f / 6.8, the RC design is f / 8. This is not important for stars, but it can easily reduce the exposure time when photographing extended objects like nebulae.

#### Does the CDK manufacturer compare apples with pears? We don't think so!

When you are comparing the new CDK with a conventional RC system, both systems are considered without additional corrector optics. However, a lens correction system is already integrated in the basic concept of the CDK. But this has nothing to do with a universal corrector. The correction system is fully integrated into the optical design and makes an uncompromising imaging performance possible all over the perfectly flat field, all the way out to the edge of a 50mm image circle.

The majority of RC users use their RC systems without additional image field lenses. Such an uncorrected RC is standard in the industry. For this reason, the CDK is compared with an uncorrected RC, because a corrector for the RC is only available for (appreciable) extra charge - if at all.

Previous CCD camera series had, as you known, at most APS format (15 x 22mm). Therefore the problem of image field curvature with the RC was hardly noticed. But the new full-frame chips dramatically reveal the distortions at the edge. In particular the image field curvature at the RC does not allow for a completely sharp image (even with perfect collimation . ) with a full-frame CCD.

The CDK is providing a solution especially for the CCD's of the new generation.

The collimation of a CDK is much simpler than that of a RC. In order to achieve the same performance as in the spot comparison under real conditions, all optical components in the RC system would have to be collimated five times better than it is necessary in the CDK design. This means that a CDK with the same tube weight has got a significantly higher temperature stability and torsional rigidity compared to the RC.

A CDK-Optics delivers the same or better performance, while it costs significantly less than the RC, especially if you have to purchase a separate corrector for the RC.

Compared to a classic RC, the CDK has got a faster focal ratio and is therefore better adapted to the smaller pixels of the newer CCD cameras.

In summary - why do we offer this optical design:
In our opinion, the CDK is a telescope which provides a better or at least comparable performance as the best RC telescopes on the market - but for less money. Due to the easy adjustability, it is much easier to use this high image quality.
Even if you consider the limitation by the omnipresent seeing, which generally makes the use of a perfect image quality with so long focal lengths very difficult, nevertheless the better adjustability and the lower price speak for the CDK. As soon as good seeing conditions or as soon as fast cameras and / or with the help of adaptive optics (- and these will become the next big thing in the imaging astronomy!) are available, a perfect collimation of the optics is very important. This will be much easier to achieve in real-life with the CDK.

It seems to us that the CDK offers you a future-proof solution for a research-friendly optics.

We are happy to answer your questions. Just send us an email to kontakt (at) baader-planetarium.de or give us a call.

52 mm Image field diameter - what does that mean?

The revolution triggered by the Planewave CDK optics is drastically documented by the fact that there are already first imitators. However - at only small price difference - a clear difference in the image field size is noticeable. The image field size of the Planewave CDK corresponds to a (real) RC-system (- however, in contrast to the RC, the CDKs give you a perfectly flat field). The flat and photographically usable field of the competitors is only 30 mm large, which is almost two-thirds smaller than expected! It would be foolish to call this a real astrograph - SC mass produced Schmidt-Cassegrain performs in the same manner. Such an XYZ optics uses the word "Dall-Kirkham" only as an advertising gag.

## Telescope optical tolerance from central axis - Astronomy

• Optical Design
• Optical Work
• Spherometer
• Spherometry equations
• Secondary mirror testing
• Foucault Tester
• Mechanical Design
• Wedge control
• Final testing
• Notes on aluminizing
• References

This page contains information I acquired during the design and construction of a 7.5" aperture F8 Maksutov-Cassegrain telescope. The telescope uses a 3-element design with a separate secondary mirror. This design form is often referred to as a Rumak or Sigler Maksutov. Design work began in September 1997, with the actual work on the optics beginning in December and being completed (except for final testing) in March 1998. The mechanical work was completed by October 1998. The following winter provided very little incentive to complete the scope (only final figuring remained), being one of the rainiest on record in Vancouver, B.C., so the project sat untouched for almost 8 months. In June th e optics were re-aluminized and the scope saw first light. The un-figured scope performed very well, but more careful collimation and testing indicated a very slight overall oblate-spheroidal figure that significantly affected the resolution at higher magnifications. This was corrected by a total of approximately two hours figuring on the front of the corrector lens.

In the fall of 2003 several improvements were made to the scope new coatings to increase the throughput, several minor fixes to allow for better collimation and the addition of a JMI motofocus assembly to eliminate problems with mirror shift. The scope made its first appearance at the Mt. Kobau star party in the BC Okanagan in July-August 2003 and was featured in Sky and Telescope's online news for August 2003 (see "Two Fine Western Star Parties").

Maksutov type telescopes and cameras have long been attractive to amateurs due to the possibility of constructing a well corrected optical system incorporating entirely (or nearly) spherical surfaces. Maksutovs employ a weakly diverging but strongly curved and thick lens at some point in the optical path, typically ahead of the primary mirror to produce an amount of spherical aberration that is equal but opposite in sign to that of the remaining optical system. Chromatic aberration is corrected by making the meniscus lens slightly diverging. If we denote the radius of curvature of the front surface of the lens by "R1" and the back surface by "R2", then the thickness "t" of the lens required to minimize the chromatic aberrations given glass of refractive index "n" is given by [4],

It is worth noting that when I derived this formula for myself I found that one must assume that the height of the traced light ray above the optical axis must be much smaller than the radii R1 or R2 for this expression to be strictly valid. In other words, you shouldn't be surprised if the results of ray tracing optimization on a Maksutov system do not agree exactly with the difference in radii (R2 - R1) predicted by this equation. Generally, the optimal difference in radii is relatively insensitive to small changes in the value of the radii R2 or R1 these radii only change with changes in the effective focal ratio of the system. Although there is room for some error in the radii of the front and back surfaces of the corrector, the tolerance in the difference of these radii is much smaller and is the most difficult tolerance to be achieved in the fabrication of a Maksutov system.

My starting design was that presented by Robert D. Sigler in the "Gleanings for ATM's" department of Sky and Telescope, September, 1975. In this design the secondary mirror is a separate optical element. This allows for greater freedom in correcting the system for aberrations across the approximately 2 degree wide field of view of this instrument. The original Maksutov-Cassegrain design of John Gregory employed an aluminized spot on the back surface of the strongly curved meniscus corrector lens as a secondary mirror. Although convenient, this design is limited to focal ratios above F15 unless an aspheric correction is applied to some element in the optical system. Commercial manufacturers often push this below F11, with F6 or lower not being uncommon in some spotting scopes or telephoto cameras. At the faster end, an additional field flattening lens is used to reduce the curvature of field inherent in these designs.

My goal in modifying Sigler's design was to reduce the length of his instrument while maintaining the aberrations to a minimum. Computer ray tracing optimization was used to find the optimal system parameters while holding the lens to primary mirror distance CP fixed as well as the effective focal length (see the diagram below for the design geometry). Two programs were used to do this: some hard-wired ray tracing code of my own, and a ray-tracing demo package called KDP (aka RoadRunner, and now Enterprise). In the end, KDP was only used to verify the results produced by my own code out of fear that KDP was converging on local minimum solutions. BTW: I now prefer to use the demo version of SynopSys for my optical designs. My own optimization code was "stupid" but robust I simply scanned all of parameter space until a best solution was found. In either case, the figure of merit used for the optimization was the RMS spot size across the field of view.

The following table is a comparison of the root mean square (RMS) spot sizes computed for my design and Sigler's design scaled to a 7.5" instrument. The spot diagram computations traced 500 rays for each of the wavelengths: 435nm, 486nm, 587nm and 706nm.

Comparison of root mean square spot sizes RSS ( in inches) for two 7.5" aperture F8 Maksutov-Cassegrain telescopes. Clicking the linked text will display the respective spot diagrams.
 Field angle RSS, Sigler (spherical) RSS, Baril (spherical) RSS, Baril (aspheric) Field position on-axis 0.00012" 0.00032" 0.00019" center of field 0.35 o 0.00021" 0.00041" 0.00033" 0.37" from o.a. 0.70 o 0.00059" 0.00097" 0.00097" 0.74" from o.a.

The theoretical diameter of the Airy disk for a 7.5" instrument is 1.28 seconds of arc, which works out to 0.00038" in an F8 instrument. Thus the diffraction limit is attained in both designs for objects on axis, although there is some image degradation near the edge of the field.

Sigler's design is clearly to be preferred in any case where the tube length is not an issue in no case was I able to match the performance of his design while shortening the tube by more than 6" (and maintaining the F8 focal ratio). Readers of Sigler's article may notice some difference in the RMS spot sizes quoted here and those implied by the spot diagrams in his article. The spot sizes here assume a flat image plane while it appears that Sigler adjusted his focus position near the edge of the field to compensate for Petzval curvature (curvature of the image plane). This analysis is valid in a visual instrument where the eye can accommodate for the small difference in focus position between the center and edge of the field (at low power). In any case, "standard" photographic resolution across the field of view at the prime focus (

0.001") is easily achieved in both instruments, assuming a flat image plane. Nearly equivalent on-axis performance of my design was achieved against Sigler's when the front of the lens was slightly aspherized to a weak oblate spheroid with a conic constant of 0.0009 (fourth column of the above table). This however does nothing to improve the off axis performance which is limited largely by Petzval curvature.

The greatest disadvantage of these instruments is the large central obstruction of the secondary mirror, which is inevitable in any fast Cassegrain with a reasonably flat image plane Introduction of a field flattening lens would allows for a more compact design, as is often done in commercial Maksutov's. The central obstruction has the effect of throwing light into the outer rings of the diffraction pattern, so that the theoretical diffraction limited resolution cannot be obtained (see [13] for a discussion of this). An F15 or slower Gregory Maksutov would undoubtedly be better suited for planetary observation in this respect. The dimensional specifications for my Maksutov are given in the table below.

 Dimension name Value in inches Clear aperture 7.5 Lens radius of curvature, concave side - R1 -10.3507 Lens radius of curvature, convex side - R2 -10.7906 Central lens thickness 0.7486 Primary mirror radius of curvature, R3 -43.356 Secondary mirror radius of curvature, R4 -23.798 Separation of lens and primary, S 20.24 Separation of primary and secondary, PS 14.342 Back focal length, Bfl 22.499 Primary mirror diameter 8.0 Secondary mirror diameter 2.84

The tolerance on R1 and R2 is ±1%, but (R2 - R1) must not differ by more than 0.1%. The tolerance on the lens thickness, primary and secondary radii of curvature R3 and R4 are all ±2%. If significant deviation is made from the prescribed radii of curvature of the corrector then retracing may be used to re-optimize the system for the new values (as long as the difference between the radii on both sides of the corrector is maintained, the design won't suffer much). It is probably a good idea to do this, even if one hasn't strayed much in the specifications. For this reason, it is best to begin working on the corrector lens rather than on the primary or secondary mirrors.

I also calculated diffraction point spread functions for on-axis imaging in my design (see diagram below). These calculations included effects due to the secondary mirror obstruction but should be interpreted with caution because the finite grid size used in the computation can introduce false periodicities in the point spread function (this can be seen for example in the point spread function plots with the focal plane 0.05" inside/outside the best focus). The important point to notice is that the point spread function is symmetric at equal distances inside and outside the focus. This contradicts certain claims that have been floating around that Maksutov systems mysteriously behave differently from other optical systems in that the diffraction disk is asymmetric on either side of the focus. If a difference is noted between the point spread functions at 0.006" inside and outside the focus this is due to the slight difference in the distances used (the lower diagram is actually slightly closer to the focus).

The 8" diameter BK7 corrector blank was purchased from Newport Glass, it had a radius of curvature of 11.4" on the convex side and 9.9" on the concave side with an edge thickness of 1.0". It was a custom formed piece costing $160 U.S. (October 1997, F.O.B.) and took 6 weeks to prepare and ship. Newport now appears to stock 6.6" blanks as part of their standard selection. A three footed spherometer was constructed using the barrel of an inexpensive ($35 CDN) 1" travel micrometer - this worked out well in the end, with readings repeatable to ±0.0001" on the same side of the corrector. In hindsight, I would seriously consider spending the extra cash for a good micrometer and leave as little to chance as possible. Originally I had anticipated measuring the difference in curvature between the two sides of the corrector using an interchangeable set of feet on the spherometer. However, when I reached the finer grades of abrasive I found that the measurement repeatability was too poor to continue using this technique. Instead I opted for a direct spherometer measurement of the concave side of the lens and indirect measurement of the convex side by measuring the curvature of the tool. The danger with this method is that one must assume that the radius of curvature of the tool matches that of the lens - this is not always true, especially if strong curvature correcting strokes have been applied prior to measurement. In order to minimize this effect, each corrective grinding spell was eased off (in the last

10 minutes) to short centred strokes.

The spherometer was zeroed on a 3/4" thick by 8" diameter plate glass flat produced using the standard three disk flat generation method (See for example [13], p.189). This glass was fine ground down to 5µm grade abrasive but not polished. Centring of the lens was controlled using the wedge control device described at this link. Wedge was controlled to within ±0.0002" (actually, probably better than ±0.0001").

The grinding tools were made of 1" square by 3/16" thick building tiles. These are the kind of tiles that are made of hard ceramic and do not have a glazed finish (the substrate used on glazed tiles is too soft). A sheet of aluminum foil was placed over the lens, the tiles laid on top of the foil (with the backing paper side down) and polyester resin ("fiberglass resin") was poured over the tiles to hold the whole thing together. A wooden disk was cemented to the back of the tile/polyester-matrix tool to provide additional thickness. These tile tools were notorious for providing hiding places for abrasive (and subsequent scratching). Recently (July 1999) I've been using a tile/plaster-matrix to grind a 10" F1 mirror and have had less problems with scratching than using the polyester matrix tool (in this case I avoided using the 5µm grade altogether). All grinding and polishing work was done by hand.

It is extremely easy to undershoot the thickness of the lens, for this reason I've provided a record of the central lens thickness at the end of each abrasive grade as guide to other workers (reference [10] may also be useful) in the following table

Record of the grinding progress during the manufacture of the lens
 Abrasive grade Thickness (inches) Work time (hours) Worked side Start 0.870 ± 0.005 --- --- #80 Carbo 0.880 ± 0.005 7 Front #80 Carbo 0.846 ± 0.005 3.3 Back #120 Al-Oxide 0.808 ± 0.002 1.5 Back #120 Al-Oxide 0.797 ± 0.002 1.75 Front #220 Al-Oxide 0.800 ± 0.002 2.9 Front #220 Al-Oxide 0.770 ± 0.002 2.0 Back #320 Al-Oxide 0.767 ± 0.002 1.5 Back #320 Al-Oxide 0.761 ± 0.002 2.7 Front #500 Al-Oxide 0.758 ± 0.002 1.0 Back #500 Al-Oxide 0.756 ± 0.002 1.2 Front 12µm Al-Oxide 0.753 ± 0.002 3.5 Back 12µm Al-Oxide 0.751 ± 0.002 1.7 Front 5µm Al-Oxide 0.750 ± 0.002 1.75 Back 5µm Al-Oxide 0.749 ± 0.002 2.3 Front

Approximate grinding rates
 Abrasive Grade Grinding rate ("/hour) #80 Carbo --- #120 Al-Oxide 0.015 #220 Al-Oxide 0.005 #320 Al-Oxide 0.002 #500 Al-Oxide 0.002 12µm Al-Oxide 0.001 5µm Al-Oxide 0.0005

A grinding schedule should be worked out as soon as the coarsest abrasive grade is completed. It is surprising how much glass is lost during the #220 and #320 mesh abrasive grades, so don't underestimate the starting thickness of the glass if you order a custom made blank.

Grinding the primary mirror to the required radius of curvature was a breeze once the corrector was done. The central hole in the primary mirror was a rather wide 2.2" in diameter so that the full (useful) 1.5"x1.5" photographic field of view would be acceptable. A thin 2" diameter brass tube was used to baffle out sky light.

In generating the secondary mirror I first cut out a 5" diameter blank from 1/2" plate glass using a biscuit cutter and #80 carborundum. The secondary mirror blank was cut out from the centre of this blank in a similar fashion (using 3" aluminum irrigation pipe for the biscuit cutter) taking care not to fracture the outer ring of glass. The secondary blank was then plastered back into the centre of the 5" disk (as shown in the photograph below) with approximately 3/16" of the groove filled with polyester resin (on the business side of the blank). The resin served the dual purpose of preventing abrasive from getting caught in the plaster and especially to provide a smooth surface that would be contiguous with the glass surface during polishing (thus reducing the possibility of a turned edge). This worked quite nicely, without producing any scratches in either the grinding or polishing stages. Once polishing was complete, the surface produced (as tested by interference against the polished out 5" tool - Foucault null tested to a sphere) was automatically quite spherical, or at least, to within 1/10th of a wave or so. The edge of the mirror was wonderfully free of any hint of a turned-down/up edge, as would undoubtedly have been the case if the mirror hadn't been worked as the core of a larger disk The initial efforts spent in preparing the 5" cored blank paid off quite nicely by the relative ease of achieving the desired optical figure.

A word of caution if you intend on using the above method of working the secondary: don't rush when you remove the polyester resin. The resin is best removed by pushing from the front once the plaster has been scraped out from the back but only do this if the resin remaining is very thin. You will chip the edge of the mirror if you rush the job. It would be best to remove the resin by chemical means, or at least weaken it enough so that it may be removed easily with a bit of scraping. I suspect that acetone may be useful in doing this (given enough time), but I haven't tried it.

Final Optical Testing and Collimation

Once the mirrors were aluminized the optics were tested by auto collimation using an oil flat. A very heavy gear oil (SAE 85W 140) was employed to damp out vibrations (vibration was definitely a problem when testing in my 3rd story apartment flat). The test appeared to indicate a system that was slightly under corrected (oblate). This was confirmed by a Foucault test on a star as well as by a diffraction ring (or star) test. The outer diffraction rings when a star was outside the focus were unduly bright compared to the outer diffraction rings as seen inside the focus. The diffraction pattern was observed with a 10 mm eyepiece and a 2X Barlow lens.

I used a petal polisher on the concave surface of the lens for one hour before re-testing the system. This produced a very marked improvement in the image quality my 10 mm 65 o apparent field of view eyepiece gave very crisp images of the moon right out to the edge of the field of view. There was no noticeable chromatic aberration. I didn't bother with an oil flat test since my previous experience had shown that the test would not be sufficiently sensitive to determine what correction if any should be applied to the system. This was partly due to vibration and air currents, but was primarily due to the difficulty of collimating the scope in its inverse position and the poor contrast caused by the low reflectivity of the oil. A Foucault star test seemed to indicate a very slight amount of over correction as did a Ronchi star test using a 55µm grid (I used nylon sieve mesh as my grating this was obtained many years ago from Small Parts Inc.). Over correction was also suggested by the asymmetry of the diffraction rings immediately inside and outside the focus, however the asymmetry now was not as marked as in the system prior to application of the petal lap. I therefore proceeded to polish the concave side of the corrector for an additional 20 minutes. The change this produced on the imaging now was not as drastic as before, however a noted improvement was observed in the brightness of the Airy disk relative to the outer rings. The Foucault and Ronchi tests on a star failed to show anything conclusive as to residual (on-axis) aberrations of the system. Another 30 minutes of polishing on the petal lap seemed to improve the diffraction disk, but this may very well also have been due to improved collimation of the optics. When testing on a 3rd magnitude star, only the first diffraction ring, a hint of the 3rd ring and the central Airy disk were visible. A very slight hint of distortion due to primary mirror flexure was also discernible but not serious.

Collimation of any catadioptric telescope poses a real challenge due to the three elements that must be aligned. This is greatly simplified by using a home-made laser collimator as shown on the left. The collimator consists of a red LED laser module from a laser pointer mounted on an adjustable plate to allow alignment of the laser beam with the optical axis of the telescope. The plate is mounted on a 2" tube in which a 1.5" hole has been drilled to allow viewing of the laser beam returning from the secondary mirror. The tube fits in the 2" focus tube at the back of the optical tube assembly (OTA). The collimation steps are as follows:

1. With only the primary mirror installed and the collimator inserted in the focus tube, the laser beam is aligned with the optical (mechanical) axis of the telescope. A plexiglass disk with a precisely drilled central hole facilitates centering the laser beam with the OTA.

2. Center the baffle tube with the optical axis (now defined by the laser beam).

3. At this point the corrector lens is installed with the secondary mount removed so that the alignment beam can pass through the hole in the corrector. If a white card is held near the radius of curvature of the corrector (about 10" away in this case), one should be able to find a point where the image of the laser spot on the card formed by the front surface of the corrector lens, is focussed on the card. With antireflection coatings this image will be dim, but it IS visible. The goal is to adjust the tilt of the corrector lens until the image of the laser spot coincides with the laser spot itself. Obviously, you'll have to guess when you're close because the image of the laser spot won't be visible when it is near the laser spot itself (which is MUCH brighter).

4. Repeat the above procedure, but now looking for the image of the laser spot created by the primary mirror - the image of the spot in this case will be further away but much brighter than that formed by the corrector. I attach a white card to a metre stick taped to the side of the OTA so that I can easily observe the reflection of the laser spot while making adjustments to the primary mirror.

5. Insert the secondary mirror and align its centre with the optical axis. The easiest way to do this (if you can't get your head inside the OTA) is to use a circular white card with 1/4" black ring drawn in its center. In my case this card was cut to fit over the secondary mirror baffle so that it was centered with the secondary mirror. The position of the beam on the card can be inspected by looking for the reflection of the card in the primary mirror, looking through the front of the telescope.

6. Finally, adjust the tilt of the secondary mirror. The reflected alignment beam from the secondary mirror should return to the laser diode. A white perforated card placed inside the collimator where the laser beam emerges is convenient for observing the reflected beam from the secondary mirror. As was the case with step 3 (and step 4 to a lesser extent), you'll have to estimate when the returning beam is colinear with the emergent one.

This collimation method consistently produces an alignment that stands up to the star test, as well as being well aligned with the OTA. Traditional coarse visual alignment followed by a star alignment, does not guarantee good results and certainly does not ensure that the optics and OTA are aligned. This alignment assumes that the focuser is aligned with the OTA. A commercial laser collimator (as used for aligning Newtonians) will quickly indicate whether this is the case. Otherwise, some means can be found to precisely align the laser beam in the homemade collimator with its mounting tube. However, this assumes careful machining of the collimator, which is definitely not the case for example shown here!

The original coatings were bare aluminum deposited by myself, using high vacuum equipment in the department of physics at Simon Fraser University in Burnaby, British Columbia. These coatings, which held up surprisingly well for several years, were replaced in November of 2003 with enhanced aluminum coatings done at Sirius Optics of Kirkeland, WA. At the same time, the corrector lens was coated with MgF2 coatings and the tertiary mirror (diagonal) was replaced with a high reflectivity dielectric mirror (97% reflectivity in visible). These improvements resulted in an estimated 40% throughput improvement over the original configuration.

I was fortunate enough to have access to a 12" lathe, 6" lathe and a milling machine so that most of the parts were machined from various aluminum and brass scrap yard findings. The goal was to produce a mounting that was both rigid and light enough for transportation. When most of the machine work had been completed, the scope was disassembled and (almost) every piece was milled to remove excess metal. The complete weight of the scope, counter-weight and tripod included, is somewhere around 100 lbs not a light 7.5" of aperture by any means.

The right ascension drive posed the greatest design problem since I wished to place the drive gear between the fork and the top R.A. shaft bearing. The advantage of this design is that it places the R.A. circle in an easy to read location and it may still be directly connected to the drive gear so that it need only be set once for each observing session. The downside to this configuration is that it increases the overhang of the fork over the top R.A. bearing and thus requires a large R.A. shaft to prevent vibration. Careful design allowed me to insert the 7" Byers gear with its friction clutch, the R.A. circle assembly and a clamp ring for manual slow-motion, while maintaining a distance of only 2.5" between the base of the fork and the top R.A. bearing. The top R.A. bearing is a cylindrical roller bearing with a 2" bore, 5" O.D. which set me back all of \$1 at the junk yard. The lower R.A. bearing uses a ball bearing with a

1.25" bore. This lower bearing supports all of the thrust directed along the R.A. axis, but this is not a problem at mid to high latitudes where most of the force on the bearings is applied perpendicularly to the R.A. axis.

The following sequence of photographs show the R.A. axis block in various states of disassembly. The diameter of the large gold ring in the first and second photograph is 9".

The photograph on the left shows the guts of the focussing mechanism focussing is achieved by moving the primary mirror. The mirror rests in a nine point flotation cell (the retaining ring above the the central perforation contacts the mirror lightly). The flotation cell rests on an aluminum bronze sleeve that slides freely but with almost no play on a brass tube that is firmly threaded into the main backing plate (the large black disk). Movement of the sleeve along the tube is restricted to the axial direction by a slot (in the sleeve) in which a small set screw has been inserted (in the brass tube). The lower end of the aluminum bronze sleeve is threaded (at 10 tpi) so that the rotation of a mating "geared nut" controls the movement of the sleeve along the central brass tube. The geared nut was fabricated from a discarded 5" (automobile transmission?) spur gear into which a (10 tpi) threaded brass ring was pressed and glued. Axial motion of the gear is prevented by a spring loaded ball bearing that presses against the top of the gear (this is what the assembly with the bare aluminum block to the lower right of center in the photograph is all about the bearing is hidden from view). The 5" spur gear is turned by a 1" pinion connected to a large 2.5" diameter focussing knob (the gold anodized piece at the bottom of the photograph). The whole sliding assembly is spring loaded by three light springs this was found to be essential to allow easy movement in either focussing direction. The focussing is smooth although it requires substantially more force than one typically finds in commercial movements of this kind. This is primarily due to the weight of the mirror which was made from a near full thickness Pyrex blank. There is a certain amount of image shift when focussing which can be troublesome when using the most powerful eyepieces (6-10 mm) but this it is not noticeable with 18 mm or longer focal length eyepieces.

In late 2003, the 2" adapter tube plate was replaced with an SCT style JMI motorized focusser, mainly to avoid problems with mirror shift when doing CCD work, but also to make the scope "friendlier" for inexperienced visitors to use. This was part of a general overhaul of the scope following the 2003 Mt. Kobau star party which included improving the mirror coatings and (up to then inexistent) lens coatings . At the same time, the baffle-tube mount was made adjustable so that it could be precisely aligned with the OTA.

The secondary mirror was mounted using a system similar to that described by Texereau [13] with the difference that an additional set of adjustment screws were included near the mirror to allow for fine tip/tilt adjustment. One should note that the three externally accessible screws adjust both the mirror tilt and mirror centring in the tube they are primarily intended for adjusting the centering of the mirror with the optical axis (not tip and tilt).

The inside of the tube (made of a piece of 10" aluminum irrigation pipe) was lined with high quality 1/2" foam of the kind used as bedding for camping. This worked quite well since the foam was sufficiently rigid to hold itself in the tube when cut to a width somewhat larger than the internal circumference of the tube. The tube was baffled by four, thin painted Plexiglas rings and the foam was lined with black velvet cloth - the baffles are not so much for cutting light as to impede air flow along the tube. A small computer fan at the top end of the tube assists in cooling the scope before use. This fan draws air in (through a filter) near the top of the scope and exhausts through the eyepiece tube. Note that if this flow were reversed, dust would be drawn into the scope unless a filter were placed over the eyepiece tube.

The setting circles were made by drawing up the tick lines in an (archaic) CAD program and importing the .DXF file to a drawing program where the tick labels could be more conveniently added. The setting circles were printed directly on overhead viewing material using a laser printer and glued to gold anodized aluminum disks. The contrast of the numbers on these settings circles is surprisingly good - in fact, they almost look good! I had been somewhat worried about reflective glare from the plastic, but this didn't turn out to be a problem: somewhat cheesy, but it works.

The tripod was made from 2" stainless steel pipe. Three folding tension bars connect the bottom of the tripod legs to prevent splaying (not visible in photograph below). Tension is maintained by tightening the gold anodized disk shown in the bottom center of the photograph above. The angle of the R.A. axis is adjusted using a 1/2" brass screw (right of center). Once polar alignment is achieved a pair of 3/8" cap screws clamp the wedge into position (i.e. the weight of the telescope does not normally rest on the brass polar adjustment screw).

The optics for the finder scope were scavenged from an old pair of binoculars. The finder was purposefully made heavy to act as a counterweight for the counterweight mounted on the opposite side of the tube (seen to the left in the above photo). The finder is mounted on the tube using a sliding dovetail arrangement so that the finder may be easily removed for transport while maintaining good alignment with the main scope. The counterweight may be adjusted in two directions by sliding along a dovetail groove mounted on the tube, or by rotating the counterweight disks about an eccentric pivot. The large thumbscrew seen in the photo (left) clamps the counterweight disks onto the pivoting block. The declination axis fine motion (right photo) is set up for both manual and motorized use. A clutch knob (hidden in photograph) engages a gear connected to a 20VDC,

1RPM motor to provide the motorized fine motion.

Useful References Concerning Maksutov Construction

[1] Cox, Robert E., "Maksutov telescope Notes", Sky and Telescope, July 1957.
-Mostly out of date information about the acquisition of material suitable for corrector blanks.

[2] Dittmer, Herman R., "Northwesterner and His Astrophotography Equipment", Sky and Telescope, June 1975, 399-405.

[3] Field, Ralph W., "Maksutovs with Subaperture Correctors", Sky and Telescope, August 1981, 166-168.
-A way to save a lot of glass!

[4] Gregory, John, "A Cassegrainian-Maksutov Telescope Design for the Amateur", Sky and Telescope, March 1957.
-About the classic Maksutov-Cassegrain design, where the corrector glass also serves as the secondary mirror.

[5] Louth, Howard, "Notes on Constructing a 5-1/2 Inch Cassegrainian-Maksutov", Sky and Telescope, July 1966, 40-43.

[6] Louth, Howard, "A Large Maksutov with Newtonian and Cassegrain Foci", Sky and Telescope, February 1977, 139-143.

[7] Maksutov, D.D, Journal of the Optical Society of America, 34(5), 270-284.
- The original paper announcing the principle of using a low power diverging meniscus lens to cancel the spherical
aberration in an optical system.

[8] Phillips, Frank W., "Aspherizing and Other Problems in Making Maksutov Telescopes", Sky and Telescope, February 1963, 110-112.

[9] Sigler, Robert D., "A High Performance Maksutov Telescope", Sky and Telescope, September 1975, 190-192.
-A design that uses a separate optical element for the secondary mirror to achieve a faster yet well corrected telescope.

[10] Tuthill, Roger W., "A Maksutov 11-Inch of Newtonian Form", Sky and Telescope, March 1964, 180-185.
-Some of useful information, especially the grinding rates to be expected when grinding the corrector lens.

[11] Wright, Franklin B., "The Maksutov Lens Applied to Herschelian and Newtonian Telescopes", in Volume 3 of "Amateur Telescope Making", Albert G. Ingalls Ed., Willmann Bell, Inc., Richmond Virginia, ISBN 0-943396-50-6.
-Obstructionless telescope employing a Maksutov corrector lens. Testing the back of the corrector lens through the
front surface.

[12] Mackintosh, Allan, "Advanced Telescope Making Techniques", Willmann-Bell, Richmond Virginia. ISBN 0-943396-11-5 (Volume 1) , ISBN 0-943396-11-3 (Volume 2) .
-Compilation of some of the better "Maksutov Circular" articles. Much practical information concerning fabrication of the corrector lens.

Articles relevant to the design of Cassegrain instruments

[12] Willey, Ronald R., "Cassegrain-type Telescopes", Sky and Telescope, April 1962.
- Comparison of various Cassegrain designs using computer ray-traced spot diagrams.

[13] Texereau, Jean, "Advantages and Disadvantages of the Classic Cassegrain" in "How to Build a Telescope", Willmann-Bell, Inc., Richmond, Virginia, 2nd Edition, ISBN 0-943396-04-2. Planetary observers should read this article before thinking of constructing a fast (faster than F13) Cassegrain.

Rutten, H. G. J. and van Venrooij, M. A. M., "Telescope Optics: a comprehensive manual for amateur astronomers", Willmann-Bell, Inc., Richmond, Virginia. ISBN 0-943396-18-2.
- Probably the best all-round reference comparing the advantages and drawbacks of the more common (and less common) telescope designs employed by amateurs.

In addition there are several archived discussions concerning Maksutov-Cassegrain design that can be found in the ATM archives.

## Abstract

The Gamma-ray Cherenkov Telescope (GCT) is a small-sized telescope (SST) that represents one of three novel designs that are based on Schwarzschild–Couder optics and are proposed for use within the Cherenkov Telescope Array (CTA). The GAmma-ray Telescope Elements (GATE) program has led an effort to build a prototype of the GCT at the Paris Observatory in Meudon, France. The mechanical structure of the prototype, known as the SST-GATE prototype telescope, is now complete along with the successful installation of the camera. We present the results of extensive simulation work to determine the optical performance of the SST-GATE prototype telescope. Using the ROBAST software and assuming an ideal optical system, we find the radius of the encircled point spread function (θ80) of the SST-GATE to be ∼1.3 arcmin (∼0.02°) for an on-axis ( θ field = 0 ∘ ) observation and ∼3.6 arcmin (∼0.06°) for an observation at the edge of the field of view ( θ field = 4 . 4 ∘ ). In addition, this research highlights the shadowing that results from the stopping of light rays by various telescope components such as the support masts and trusses. It is shown that for on-axis observations the effective collection area decreases by approximately 1 m 2 as a result of shadowing components other than the secondary mirror. This is a similar loss (∼11%) to that seen with the current generation of conventional Davies–Cotton (DC) Cherenkov telescopes. An extensive random tolerance analysis was also performed and it was found that certain parameters, especially the secondary mirror z-position and the tip and tilt rotations of the mirrors, are critical in order to contain θ80 within the pixel limit radius for all field angles. In addition, we have studied the impact upon the optical performance of introducing a hole in the center of the secondary mirror for use with pointing and alignment instruments. We find that a small circular area (radius < 150 mm) at the center of the secondary mirror can be used for instrumentation without any significant impact upon optical performance. Finally, we studied the impact of reducing the size of the primary mirror for the prototype telescope and found that this comes at the cost of poorer image quality and light collection efficiency for all field angles, but at a significant cost saving for a one-off prototype.