The Cassegrain Project
The Cassegrain telescope is probably the first type telescope that the ATM would like to make after mastering the basic Newtonian telescope. In this article I will show how it is possible for the ATM to make his own Cassegrain telescope. Mostly featured is my 12.5 inch f/20, however some photos are from a similar 10 inch telescope (this article is not intended to provide detailed instructions.)

Definition of the Cassegrain Telescope
The Cassegrain optical configuration was first defined by Laurent Cassegrain around 1672, a French Catholic priest who taught science classes at the College de Chartres, a high school level institution The Cassegrain configuration is a reflecting telescope characterized by two mirrors with optical power, located coaxially on the optical axis. The primary is a concave mirror and the secondary is convex and placed inside the primary focus. The secondary reflects the light back toward the primary. Depending on the curve of the secondary, the light can, and most often does, come to focus behind the primary having passed through a hole in the the primary.

In its most common form, the primary is a relatively short focus mirror and the secondary is designed to expand the light cone providing magnification. As originally conceived, spherical aberration was corrected by using a parabolic primary and a hyperbolic (convex) secondary. This is referred to as the classical Cassegrain. System focal ratio and central obstruction size are parameters that the optical designer can control based on the focal ratio of the primary and magnification of the secondary.

As optical designs matured, it was discovered that spherical aberration can be corrected by several combinations of figures for the primary and secondary mirrors.  However, with the two degrees of freedom of the two mirrors, a second aberration, most often coma, can be made more severe or improved. Non classical Cassegrain arrangements bear the names of the designers who discovered them. The Dall – Kirkham, for example, is a non classical Cassegrain in which the secondary is spherical, and the primary is elliptical. This arrangement corrects spherical aberration at the expense of significantly increased coma. The Ritchey – Chretien, on the other hand, has two hyperbolic mirrors so chosen that both spherical aberration and coma are corrected. In a classical Cassegrain the coma is the same as a Newtonian having the same focal ratio as the system focal ratio of the Cassegrain.

Additional optical elements can be added to the arrangement to correct for spherical aberration. The most commonly added elements are a Schmidt or Maksutov corrector at the light path entrance. These correctors are refractive elements. Cassegrains of this type are often referred to by a double name including the corrector type, such as a Schmidt – Cassegrain, or Maksutov Cassegrain.

This article will feature a 12.5 inch Classical Cassegrain with parabolic primary and hyperbolic secondary

Advantages and Disadvantages of the Cassegrain
The advantage of the Cassegrain is that it allows for a long focus telescope in a relatively short tube. It also allows for the eyepiece to be placed at the rear of the telescope which is considered to be a more convenient location. Long focus has the advantage of increased image scale, thus providing high magnification with modest eyepieces. Eyepieces perform better and the overall eye relief is more comfortable.

The most significant disadvantage is that the eyepiece points directly out the front of the tube, thus allowing any stray light that comes around the secondary to go directly into the eyepiece washing out contrast. Other disadvantages include that Cassegrain telescopes end up with a rather high focal ratios in order to keep the central obstruction small. And the optics of the Cassegrain are relatively difficult to make. The primary is usually approximately f/4 which is difficult to accurately parabolize, and the convex secondary is difficult to test without auxiliary test optics.

The disadvantages can be mitigated making the Cassegrain a very practical telescope. The stray light issue can be reduced with baffling. Current CCD images can be processed to replace the contrast washed out by a large secondary, therefore allowing imaging Cassegrains to be shorter overall focal ratio. And fabrication difficulties can be reduced by using modern testing techniques or making simplified versions such as the Dall – Kirkham.


A Practical ATM Design
Although the Cassegrain optical arrangement will allow almost an infinite combination of primary mirror focal length and secondary ROC there is a range that is most practical for the ATM to consider. As a general rule, the shorter the primary focal length, the faster the system focal ratio can be while maintaining a secondary diameter that results in a central obstruction where contrast is still acceptable. The general rule for central obstruction is to stay at or less than 30%. *(see footnote). The design must also account for back focus distance or the distance from the primary mirror to the focus plane behind the telescope to accommodate the focuser, star diagonal, and eyepiece. Considering the primary mirror focal length, the shortest, or fastest focal ratio generally accomplishable by an advanced ATM is f/4. I chose f/4 for the primary. Once chosen, Cassegrain mathematics ends up with f/15 for a central obstruction of 30%. Or, a higher system focal ratio yields a smaller central obstruction. I chose f/20 for detailed planetary use.

Mathematics for calculating the optics radii and spacing is readily available in the literature. It is also possible to download simple to use programs for designing Cassegrain systems. If you are a do-it-yourselfer like me, I used the equations in Texereau’s book and made a simple EXCEL spreadsheet. I simply input the primary diameter D1, primary focal length f1, back focus distance, and desired system focal ratio and voila the spreadsheet spits out the rest.


Cassegrain design

 

 

 

 

 

 

 

 

 

input

 

input

 

 

 

 

 

 

input

input

 

D1

D2

f1

r2

F

M

p

p1

d

e

Fr

%obs

12.50

2.47

48.81

23.88

253.94

5.20

9.64

50.17

39.17

11.00

20.32

19.76

 

 

 

 

 

 

 

 

 

 

 

 

D1=diameter of primary mirror

p=length of primary light cone cut by secondary

 

 

D2=diameter of secondary

 

p1=distance from secondary surface to system focus

 

f1=focal lengh of primary mirror

d=primary surface plane to secondary plane (=f1-p)

 

r2=radius of curvature of secondary

e=distance from primary surface to image focus behind primary

F=system focal length

 

p=(f1+e)/(M+1)………………Texereau eq 27

 

 

M=magnification = F/f1, =p1/p

p1=p*M…………………………………….eq28

 

 

Fr=system focal ratio

 

r2 = 2*p*M/(M-1)………………………….eq 29

 

 

 

 

 

 

D2 = D1*p/f1………………………………eq 30

 

 


Above is what my EXCEL spreadsheet looks like for my 12.5 inch f/20 Cassegrain. You will have to increase the secondary diameter to increase your unvignetted field of view beyond a point using Texereau’s formulas. I added about 0.300 inch for a D2 of 2.77.

Making the Primary
Making the primary is similar to making a Newtonian primary except it is a fast focal ratio and has a hole in the center. I chose a 12.5 inch diameter, 2 inch thick annealed pyrex blank for the primary mirror. I rough ground the f/4 curve using standard grinding techniques on a full size tool made out of porcelain tiles epoxied onto a form made of cement. After roughing in the curve, I trepanned a 2.5 inch diameter core from the back using a holesaw, with teeth ground off, and 120 grit abrasive and a standard drill press as shown on the right. These days, diamond impregnated cutters are readily available and cut through faster. I ground to within 0.150 of the curve surface on the front then finished cutting out the center core from the front after the mirror was polished and final figured.

In order to obtain the best possible figure, I tested the primary using the autocollimation test. This test uses a perforated optical flat near the light source. The light source is at the mirrors focus (rather than the center of curvature) and the light passes through the perforation in the optical flat to the mirror being tested. The light then reflects back in a collimated beam the diameter of the mirror being tested. The light is intercepted by the optical flat and reflected back to the mirror being tested which refocuses the beam through the perforation to the Ronchi screen or knife edge for viewing. This test produces a null return such that a knife edge would show a smooth uniform cutoff and Ronchi lines would be straight and parallel. At left is a picture of the autocollimation set up. The flat is to the left. The light source and Ronchi screen are behind the flat and cannot be seen. The mirror being tested is to the right. Also in the picture is a TV monitor. At the Ronchi screen is a TV camera so the test return can be viewed easily on a TV.

To the right is what the finished primary looked like tested by autocollimation. The picture is a mosaic of about 6 TV camera images to capture the entire 12.5 inches of the mirror. The triangular divits on the left and right edges are artifacts of making this mosaic.

Now that the primary is finished, it can be coated so that it can be used for subsequent tests of the secondary.


Making the Secondary
The unique part of making a Cassegrain is making the secondary. The blank needs to be made and testing the finished mirror involves different techniques because it is convex. Jean Texereau in his book “How to Make a Telescope” includes an intereference method of testing the figure of the secondary. His technique will be used here, but also used will be a system autocollimation test.

Most often the blank, itself, needs to be made because it is not common to find suitable pyrex (or similar) material in a size that fits your design. I trepanned my blanks from 1/2 inch thick Schott Borofloat sheet using a three inch hole saw (teeth ground off), 120 grit and water. I prepared four such blanks. One for the mirror, one for the tool, another for the tool pitch lap, and the fourth for the mirror pitch lap.


Grinding the secondary is just like grinding any other optic except in minature. I ground the secondary with the mirror on a workstand and worked the tool on top just like I would grind a larger mirror. This optic is small enough that a lens grinding machine could work well. I did not have a lens grinding machine and it is not necessary if you do not have one. Keep in mind that the convex optic, which is the optic on the bottom, is what you want for your secondary. It is important to have a good sagitta measuring instrument because the ROC is critical to the design. A small change in ROC will affect the mirror spacing and focus location.

When it comes to polishing, both the tool and the mirror get polished. The tool gets polished only enough to get a reflection and insure that it is a good sphere. The tool is used to get a good measure of the actual ROC by knife edge on the test bench and later to establish that the mirror matches that radius and is spherical. Shown at the right is a Ronchigram of the tool showing a perfectly spherical figure.

Then the (convex) mirror is polished out completely and figured so that it matches the tool in both radius and a good sphere. When the convex mirror matches the already measured tool, the intereference fringes will be straight and parallel. Slight overall curve in the lines indicates that the curves don’t exactly match in radius and this is OK provided the fringes are smooth curves. Shown at the right is an intereferogram showing the stage where the convex mirror has been figured to match the tool in radius and a good sphere.

Next the optical tube is constructed. Details of the OTA construction will be summarized later, but for now we need to run an autocollimation test of the entire telescope system to put the final hyperbolic figure on the secondary. To do this, the telescope is placed on the test bench with the autocollimation flat just forward of the front of the telescope. The light source and Ronchi screen is placed in the focuser drawtube and the focuser knob can position the source and screen inside, outside, or at focus as necessary to conduct the test. This test has five reflections. The light leaves the source, reflects off the secondary to the primary, reflects off the primary in a collimated beam to the autocollimation flat, reflects off the autocollimation flat back to the primary, reflects back to the secondary, reflects back to focus at the Ronchi screen. Shown to the right is the test set up. The autocollmation flat is seen to the right. The TV camera is behind the Ronchi screen.

Right is a Ronchigram of the secondary, seen through the autocollimation test, before figuring to the hyperbolic shape. It is spherical as shown by the interference test earlier. In this test, with the Ronchi screen outside of focus, the outward curving Ronchi lines, indicating initial over correction, are apparent.. The washed out white spot is the direct reflection of the light source. Unfortunately this extra reflection is a nuisance.

Figuring the secondary is opposite to figuring a concave primary mirror to a parabola. What needs to be reduced is the area between the center and the edge. This is a bit tricky. Particularly, getting the region just inside the edge without turning the edge. To the right is shown a polishing lap called a petal lap. This lap is formed so that the 70% zone sees the most pitch lap area and concentration with progressively less lap going to the outer zones and to the inner zones. Several shapes of petal laps may need to be used to get the figure good and zone free. The dark seen in the picture is the pitch. The tan is Cerium oxide in the void regions.

After the secondary is figured to the required hyperbola, the Ronchi lines shown by the Autocollimation test will be straight and parallel. At the right is shown the autocollimation test of the system with the finished secondary in place.

There is a slight problem with figuring using the system autocollimation test. The secondary is sized for increased unvignetted field of view of some defined size by the design. The system autocollimation test uses a point source of light which refocuses to a point. This means that the edge of the secondary can not be seen by the test. As a back up additional test, the secondary was interference tested against the tool. This way, the hyperbolic shape is confirmed and, in addition, the edge of the mirror can be seen. The picture on the right shows the interference test of the finished secondary against the spherical tool.

The interference test technique for a Cassegrain secondary against a reference sphere was published by Jean Texereau in his book “How To Make a Telescope”, 2nd edition, by Willmann-Bell. I recommend that you read his section. There is an interferogram in that section that shows his finished secondary tested against the spherical tool. If you look at that picture, you should see an image very similar to the picture above. Texereau explains how to measure the edge slope and 70% zone curvature away from a reference straight line to verify that the hyperbola is the correct conic constant. Since I used this test as a qualitative additional test, primarily of the edge, these measurements were not made. The autocollimation test established that the conic constant is correct.

The Hindle Sphere Test
A far better and more convenient way test the secondary is by using a Hindle sphere. This telescope was made before I had made a Hindle sphere tester. The notes above show how you can also make a Classical Cassegrain without it. I have a Hindle sphere tester now, however, and have made a new improved secondary using this tester. I invite you to read my article about it located here....


Making the Optical Tube
There are likely as many ways to make an optical tube for a Cassegrain as there are ATMs who build them. The OTA need not be much more difficult than making a tube for a Newtonian, it is just different. One parameter that the OTA should accommodate is a provision to vary the distance between the two mirrors. Slight differences in this inter mirror distance results in several inches difference in the focus location, and the spacing of the mirrors has an effect on the correction for spherical aberration.

I used a sonotube for the tube. I made the primary mirror cell out of Ύ plywood. The cell has wings, the OD of which match the ID of the tube thus the mirror cell and mirror are held centered in the tube. Each of the three wings has a threaded “T” nut in it. The tube has three equally spaced threaded rods anchored by a bushing four to five inches forward of the front surface of the mirror. The mirror cell is threaded into position with the “T” nuts in the wings riding on the threaded rods. The threaded rods protrude past the telescope backing plate and the end sized so that once the backing plate is in place knobs can be put on the rods. With this arrangement, the primary mirror can be moved and collimated while viewing through the eyepiece.

To the right above is the primary mirror in the cell. There is a masonite ring around the mirror perimeter and six screws that hold the mirror between the ring and the mirror cell. The cell is Ύ inch plywood that has been varnished, sanded smooth, then painted black. A shop Vacuum conical nozzle has been fitted to the central perforation of the primary mirror as a primary baffle. This is not ideal, but it does work. I've since upgraded the baffling in this telescope. If you're interested, you can read about it here...

Directly to the right is the mirror and cell in th eOTA without the backing plate. Easily seen are the three threaded rods protruding through the "T" nuts in the mirror cell wings. These threaded rods will protrude through the backing plate and the holes in the backing plate act as crude rear bearings for the rods

To the right is the telescope with the backing plate in place. At the time of this photo, the parts had not been finished so the nature of the sonotube and plywood backing plate are obvious. The focuser is mounted to a thin board and the backing plate has wood strips so the focuser can be slipped out for transport and so the focuser can be used on other telescopes.

The secondary spider was simply made from a wood center with three thin aluminum vanes epoxied into the wood center. The OD end had long nuts exposed to the vanes so the vane ends can be held by screws coming in from the tube OD. The wood center of the spider has three screws between the vanes that push on the wood circle that actually holds the secondary. These screws are so the secondary can be collimated.

After installing the secondary, there's not much more to it than some paint and finishing touches. I hope you've enjoyed reading about this project and perhaps might be interested to give it a go yourself. Below are photos of the finished product.


Photos of the Completed Telescope