Optical Testing of Parabolic Mirrors

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Introduction: Optical Testing of Parabolic Mirrors

About: I'm an aerospace engineer by trade but am interested in astronomy, robotics, CNC machines, Arduinos, you name it.

If you are building a telescope or if you want to see if a telescope primary mirror has a good 'figure' before you buy it, you need to perform an optical test of the mirror.

A properly figured primary Newtonian mirror is a near-perfect parabola. How close to perfect does it need to be? A good telescope mirror has less than 1/4 wavelength of light error on its surface! This means that the surface imperfections should be smaller than 100 nm.  This is a very small margin for error but amateurs telescope makers can achieve this and better if they are persistent and careful.

In order to test the figure of the primary mirror we must build the following:
Mirror mount,
Optical tester,
Optical mask

Then I'll describe how to use these tools to determine the figure.

Step 1: Theory of Operation

The 100 nm accuracy of the surface requirement is a very tight tolerance and can not be measured directly using such things as rulers or depth gauges.  These tight tolerances can indeed be achieved using normal hand tools by magnifying the surface angles.  We can find the focus point of the mirror by shining a narrow slit of light onto the mirror and observing the shadows as a knife edge is passed in front of the returning light.

Let us assume that we have a perfectly shaped spherical mirror and our knife edge is near the focus point of the mirror.

See Figure A.
Looking down from the top, if we illuminate the mirror at the focus point the light will hit the mirror and return exactly to the focus point.

See Figure B.
If we move a knife edge inside the focus and on the right, the knife edge blocks the light returned from the right side of the mirror and does not affect the light from the left side of the mirror.

See Figure C.
If we move the knife edge outside the focus and on the right, the knife edge blocks the light returned from the LEFT side of the mirror.

So, when the knife edge is inside the focus, moving the knife edge left and right makes a shadow move across the mirror in the same direction as the movement of the knife edge.
When knife edge is outside the focus, moving the knife edge left and right makes a shadow move across the mirror going in the opposite direction of the knife edge.
When the knife edge is exactly at the focus point and the knife edge is moved from left and right, the mirror dims uniformly, i.e. the shadow doesn't appear to move left or right but the entire mirror dims.

A good telescope mirror does not have a spherical shape but a parabolic shape. For a parabola, the outer areas of the mirror focuses farther away from the inner areas of the mirror. We can therefor use this knowledge to determine the precise shape of the mirror by finding the focus points of each area of the mirror.

Step 2: Tools and Materials

Tools:
  Table Saw with dado blade,
  wood chisel
  screwdriver

Materials:
(Note: all of my dimensions are in US units.  Metric equivalents are perfectly fine.)
  For Mirror Mount:
    3 foot by 1.5 foot plywood, 3/4 inch thick
    2 foot by 1.5 foot plywood, 3/4 inch thick
    2 6 inch angle brackets
    1  L hook
    12 screws 3/4 inch long for the L brackets
    3 flat head wood screws for 'feet'
  
  For Optical Tester:
    6 inch wide by 32 inch long by 3/4 inch thick hardwood board
    3 single sided utility blades
    2 magnets 1/2 inch diameter
    1 depth gauge with 1 inch or more of travel with readings every .001 inch
    Small bright bulb or LED  (I used a krypton bulb)
    6 inch 3/32 inch thick or better metal angle iron
    6 inch 3/32 inch think flat metal iron, 1 inch wide
    2 1/4 inch threaded rod, 20 threads per inch, 3 inch long
    2 knobs that fit 1/4 inch threaded rod
    4 springs
    miscellaneous wood screws and glue

  For Couder Mask:
    1 light-weight cardboard large enough to cover the mirror being tested.

Step 3: Building the Mirror Mount

A mirror mount is needed to hold the mirror during testing. 

If the mirror is a 'thin' mirror (i.e. the thickness is much less than 1/8th its diameter) then the mount must hold the mirror without deforming it.  The weight of the glass can deform a thin mirror.

In my case, I was making a full-thickness mirror, which is a mirror whose thickness is 1/8th the diameter or more, so mirror deformation was not an issue.

If mirror deformation is a factor in your use, you may want to replace the two wood blocks I used with a leather strap which distributes the weight of the mirror across the entire bottom half of the mirror.

The mirror mount I made is shown in the attached pictures.

Step 4: Build the Optical Tester

The optical tester is a device which shines a slit of light onto the mirror and finds the focus point of each area of the mirror.

It is essentially an X-Y table with a 1/1000th of an inch accuracy in the X dimension.

First Construct the base,
Construct the middle layer,
Construct the top layer and assemble,
Add the light source and the depth gauge.

 

Step 5: Construct the Bottom, Middle, and Top Sliding Boards.

Pictures are worth a thousand words so I hope you can tell what I did form the pictures because my words are probably a little confusing.


I used three 6 inch by 7 inch, by 3/4 inch pieces of wood, one for the bottom plate, one for the middle plate and one for the top plate.

Using a dado blade in my table saw I carefully cut a slot into the board just wide enough to hold a wood slat and deep enough so that slightly less than 1/2 the depth of the wood slat is protruding when placed in the slot.

I then cut a similar slot in the middle board.  When the slat is inserted into the base slot, the slat will lay inside the slot in the middle board and allow the boards to slide in only one axis.

On the other face of the middle board I cut a similar slot that is rotated 90 degrees from the first slot.

On the top board I cut a similar slot so that a slat placed into the middle board's slot and the top board's slot allow the top board to move perpendicular to how the middle board moves.

Place two slats in and glue them only to the middle board this allowing the boards to slide.

Step 6: Complete the Base

Complete the base by adding three 'feet' so the base sits very stable.

Add an arm that holds the light slit.

Add a metal plate with a 20 threads per inch bolt so that the middle and top plates move when the bolt is turned.

Add a .001 inch dial gage to very accurately tell how much the top and middle plates have moved.

Add a spring to hold the middle plate against the threaded bolt.

Step 7: Complete the Middle Plate

Add a plate attached to the middle plate that hold a 20 threads per inch bolt that presses against the top plate moving it perpendicular to the other bolt.

Add an arm with a utility blade to the top plate so that when the bolt is turned the blade 'cuts' the light returning from the mirror.

Add a spring so the top plate is pressed against the bolt.

Step 8: Using the Device.

Place the mirror being tested in the holder and the optical tester at twice the mirror's nominal focal point.

Shine a slit of light from the tester to the mirror and back again.  Proper positioning is critical.

As mentioned before, when the top plate is moved the utility blade cuts the light returning from the mirror.
When moving the knife edge from left to right, if we see the mirror darken from left to right also then the knife edge is inside focus.
If the darkening moves opposite the knife edge, then the knife edge is outside focus.

Since we want the mirror to have a perfect parabolic shape, we measure precisely the focal points of each area of the mirror.
To help us focus on areas of the mirror, we make a couder mask.

A couder mask has little windows cut out that expose sections of the mirror.  For example, the couder mask will have windows for the outer 1/2 inch of the mirror.  Another set of windows expose the next inner 3/4 inch of mirror.  Ideally as the windows expose mirror surfaces closer to the center the window gets larger.  This is because we want each window to represent equal amounts of light entering the eyepiece, and at the outer edges the area is larger due to the larger circles of the window.

To build a couder mask we start by deciding the outermost dimensions of R1 and R2.  We then compute R3 so that the circles exposed represent equal areas of the mirror.  We continue for R4, R5... and so on until we reach the center of the mirror or so.  The centers of  newtonian mirrors are in the shadow of the secondary mirror and they really don't contribute much light.

Step 9: Optical Testing

I couldn't find any good videos of the mirror testing.  I have the following video which just shows how the shadows move over the surface.  As you can see this mirror has a rather large hole in its center.  If you use the mask, you can watch the shadows and record their positions to the nearest .001 inch.  You then compare the actual results with the perfect parabola.  If you are building your mirror you then change the polishing strokes and retest allowing time for the mirror temperature to stabilize, keeping good notes of the results given your polishing strokes.  You can then keep polishing using the techniques that move the mirror surface closer to a parabola.

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    18 Discussions

    At which point of the mirror grinding and polishing process do you begin foucault testing?

    I am currently working on my first mirror a 9 3/8" dia f5.9 ground down to 5 microns.

    1 more answer

    During the rough grinding process you are simply trying to 'hog' out the glass to get the rough figure close to the desired focal point. Here we can use the 'spit test' which uses the foucault tester to simply measure the focal point of the majority of the mirror and then you spit on the ground, i.e. you mark the focal point very roughly to ensure you're deep enough to begin the next phase. After hogging out the mirror then you use finner and finner grinding grits to remove the scratches in the mirror from the previous step. During this phase you are averaging out your strokes to keep the mirror figure roughly spherical. As soon as you transition to polishing is where I begin to take real measurements and good records. Each person's hand pressure is different so you must 'learn' how your particular strokes are changing the mirror figure while polishing. Books may guide you but you can't rely on them blindly due to this variance in each person's polishing strokes. You may find that in order to reduce the 3/4 diameter ''ring' you have to do some funny 'W' stroke where the center up-down stroke is smaller than the outer legs. Essentially you record what your strokes do to the mirror figure and you use that knowledge to move the figure closer to the ideal. Be sure to allow the mirror to cool as the polishing strokes can heat the surface, changing it so that it tests well right after the strokes but then get out of figure after the mirror cools.

    During the polishing phase it is a contest between how much polishing you can stand against your desired level of perfection. I recall 'fondly' of doing one more little polish to make the mirror a little better and making the mirror worse only to have several hours of work to bring it back to its original level of 'goodness'. :-)

    The feeling is great when you finally call it Done.

    Best Wishes!

    Clearly the smaller the error the better.

    I said the error has to be less than 1/4 wavelength and thereby set an upper bound to the figure error. Defining the 'best value' was not the purpose of the instructable.

    Best Wishes

    0
    user
    nobby2

    1 year ago

    Thank you for the concise explanation. I have recently built a Foucault tester based on the Stellafane model and have 3 different Ronchi slides which appear to be doing the job.

    My problem is despite following all the steps of testing I just cant get the expected knife edge shadow using a blade glued to a 2 inch x 2 inch slide. I have the correct Radius of Curvature etc.

    I keep on reading that the light, in my case an LCD as per the Stellafane model should be shining through a narrow slit. There was not mention how the slit is constructed and used.

    My Ronchi Slide when approaching the ROC almost behaves like a knife edge and I do get an image of what looks like the surface of the mirror.

    I should add the mirror I am using is a completed silvered 8" being used for testing only.

    2 replies

    I implemented my knife edge by drilling a hole into the support 'stick' just large enough for the lamp to sit inside. I then glued one blade of a straight utility blade over the hole so it cuts the center of the light. I then added magnets above and below the light that would stick to the first and second blades allowing them to be adjusted.

    Appreciate your reply. Thank you. Gives me something to think about..

    This is a great explanation of the results of the knife edge test, which for some reason are very hard to find. Lots of people talk about this device but don't explain what the results indicate. My mirror has issues, but now I can (maybe) pinpoint them. Thank you for this.

    1 reply

    decades ago when i was doing my own mirror, one had to do that with the ' Foucault test' and basically just eyeball it, which I never could grasp. This seems to be the same principle but with a bit more measuring behind it. Great

    1 reply

    Yes, this method requires precise measurement to achieve the 1/4 wavelength or better surface. Thanks.

    At last some easy way to do tjis. From many years I wanted to build a telescope, but this part of the process allways stoped me. Now I dont'n have but to start.

    1 reply

    The WEB has a lot of information that can help you. One noteworthy site is: http://stellafane.org/tm/atm/index.html

    Best Wishes!

    Very nice.
    I got an education as i didn't know about measuring a mirror's focal point or even a tool to do this.

    1 reply

    Great instructible! I never understood how people could grind their own mirrors, but this makes sense.

    1 reply

    Thank You. This is one of those instructables I started over a year ago and thought I'd just finish it up. It is amazing to me that Sir Isiac Newton and others knew these techniques many many years ago.

    The grinding process (not discussed) employs a glass or ceramic 'tool' rubbed against the glass disk with successively finer grits of aggregate and water.

    To actually polish the glass to a smooth figure you use pitch which I believe is a petrolium product. It is like a very think liquid, hard to the touch but yet maluable as you can leave a mark with your thumbnail. How it works is still a bit of a mystery to science (so I'm told) but it appears the glass is melted and refrozen on a microscopic scale as the tool with the pitch layer is rubbed against the glass disk.

    Thanks again for the nice comments.

    Best Wishes