A full-aperture optical test
for large convex secondary mirrors:

Step 1. Proof of concept

May 1, 1993

Jim Burge and Dave Anderson

Steward Observatory Mirror Lab

University of Arizona

Technical Memo

UA-93-04


http://medusa.as.arizona.edu/lbtwww/tech/ua9304.htm

A new technique for testing convex aspheric secondary mirrors is being developed at the Steward Observatory Mirror Lab. This test will use a full-aperture test plate with a computer-generated hologram (CGH) fabricated onto a spherical reference surface. The interference between a test beam reflected from the secondary mirror and a reference beam diffracted from the CGH will be used to test the secondary mirror. This method of testing, which is similar to the Fizeau test, was verified on a small scale in the laboratory and shown to be highly accurate. The interference pattern was shown to have excellent contrast and also to be largely insensitive to vibration and air currents.

A flat optic with 8.3 nm rms figure error over a clear aperture of 11 mm was measured using a diffractive test plate. The error in making the measurement with the CGH test plate was determined to be 2.1 nm rms with contributions from two independent components. The distortion in the CGH caused a measurement error of 1.9 nm rms and noise in the measurement from laser speckle and stray reflections in the camera caused an additional 0.5 nm rms error. The optical test of secondary mirrors using the CGH test plate will have similar errors due to the CGH distortion, but a rotating ground glass screen will be used to eliminate speckle and spurious fringes. On the basis of this data, we are highly confident that the CGH test plate will provide an efficient method for making highly accurate surface measurements of secondary mirrors.

Introduction

As a first step in the development of this test, the method of using a CGH with a test plate was demonstrated on the one-inch scale using flat surfaces. The test was set up to simulate the CGH test plate for a small, off-axis piece of a secondary mirror. The test was shown to accurately measure surface errors to 0.0015 l rms. The principle of the CGH test plate method for secondary mirrors, shown schematically in Fig. 1, uses a concave spherical surface as a beamsplitter and reference surface. The test plate is illuminated with light that refracts from the reference sphere to strike the secondary mirror at normal incidence. This light reflects back onto itself to form the test beam. Any figure errors in the secondary mirror will be imparted to this test wavefront. The reference wavefront is formed by diffraction from the ruling on the reference sphere. The CGH is designed to make this reference beam match the test wavefront so it also retraces its path. (This is known as a Littrow configuration for a grating.)

The spherical surface forms the reference for this measurement, so its shape is critical. Since this is a concave spherical surface, it can be measured interferometrically from its center of curvature to high accuracy. Any shape errors in the reference sphere will be subtracted from the secondary test results.

The small-scale laboratory test used this configuration, but was simplified with the use of flat surfaces. By using flats, the fabrication of the CGH could be performed using standard photolithographic techniques and the surface figures are well known. Since the CGH for a tilted plane is just a straight line ruling, it is easily specified. Also, all of the diffracted orders from a straight line ruling are plane waves with the tilt angle proportional to the order number. By testing the plane wavefronts from different orders, the surface figure and ruling errors are fully separable.

The accuracy of the wavefront created by the CGH is directly related to the positional accuracy of the lines and the order of diffraction. The error in the diffracted wavefront is simply

( W / ) = m ( x / s)

where x is the error in grating line position, s is the local grating spacing, and m is the order number. This error is added to the wavefront error that comes from the surface figure of the CGH substrate. All orders are equally affected by the surface figure.

Description of test

The test setup, shown schematically in Fig. 2, was used to demonstrate the accuracy of testing with a holographic test plate. The geometry of the secondary test was preserved in this prototype as much as possible. A collimated HeNe laser beam was set at normal incidence to a /4 test flat. The wavefront reflected from the test flat formed the test wavefront. Diffraction from the linear ruling was used to create the reference wavefront. The interfering beams were brought to a focus and passed through a 200 µm pinhole to block the undesired orders of diffraction. The resulting interference pattern was projected onto a CCD camera for evaluation.

The rulings, made by Klarmann Rulings, Inc., consist of aluminum stripes covering an area of 14 15 mm fabricated onto a flat glass (BK7) substrate. Two rulings were made and tested -- one with 100 µm spacings and the other with 200 µm spacings. These spacings correspond to actual spacings that will be used in the secondary mirror test. The duty cycle, or ratio of metal band width to center-to-center separation, was fixed at 15% for both rulings to maximize the contrast of the interference pattern.

Accurate, high resolution measurements were made using phase shifting interferometry. The test flat was mounted to a PZT that provided the motion for the phase shifting. The phase measurement was performed using software from Phase Shift Technology running on a 486 PC. Errors in the phase measurement are below 0.5 nm for an average of 10 maps.

The retro-reflected beam off the test flat was used as feedback to align the light to be normally incident onto the test flat. The ruling was then tipped to make the desired diffracted order coincide with the test beam. The position of the 200 µm pinhole was adjusted to pass these two beams, but to block all of the other orders. The CCD camera was placed at the image of the test flat where diffraction effects are minimal.

Results

The use of the CGH test plate was shown to have the high accuracy that was predicted. The fringes of interference had virtually perfect contrast and were easily phase shifted. There were some high frequency intensity variations caused by reflections from the window on the CCD and from laser speckle. These will be eliminated in the secondary mirror test by imaging onto a rotating ground glass disk and re-imaging onto the detector. Any other high frequency errors will be reduced by averaging several measurements and rotating the test plate.

The CGH was tilted to the appropriate angle to allow measurement of the test flat using the -1, 0, +1, and +5 diffracted orders. By using the fact that the CGH distortion causes errors proportional to the order number, the surface figure and the grating writing errors were separated. As expected, the surface figure computed using all four maps is virtually identical to the measured zero order. A contour map of the test flat surface figure with respect to the reference surface is shown in Fig. 3.

The measurement of the test flat with the first diffracted order from the CGH is shown in Fig. 4. This corresponds to the measurement of a secondary mirror with a CGH test plate. The difference between these two gives the error in the measurement, shown in Fig. 5.

Fig. 3. Surface figure of test flat. The figure errors are 8.31 nm rms and 40.8 nm P-V. The contours shown are at 5 nm intervals.

Fig. 4. Measured surface figre using the first diffracted order from the CGH. The figure errors are 7.60 nm rms and 38.3 nm P-V. The contours shown are at 5 nm intervals.

The measurement error shown in Fig 5. has two components -- noise in the measurement and distortion in the CGH. These two effects were separated using measurements at several orders. The CGH distortion was determined to cause 1.92 nm rms figure error. The noise in the measurement, caused mostly by the spurious fringes from the CCD window, was determined to cause 0.54 nm rms error.

The distortion in the 200-µm pitch ruling required to cause a surface figure error of 1.92 nm rms and 12.2 nm P-V was calculated. The distortion in the ruling was 1.2 µm rms and 7.7 µm P-V with a spatial distribution shown by Fig. 5. This amount of distortion is consistent with the claims of the company that fabricated the rulings. It is also comparable to the writing accuracy expected in the fabrication of the test plates.

Conclusion

An experiment was performed to verify the technique of using a test plate that has a CGH drawn on the reference surface. The test was simplified by using flat surfaces and linear rulings, but the ruling pitch, illumination and imaging geometry, and measurement by phase shifting simulate the optical test of secondary mirrors. This test showed that optical testing with a CGH test plate gives high contrast fringes that are insensitive to vibration and air currents. A ruling with distortion errors of several microns was used to measure the surface figure of a small flat to an accuracy of less than 2 nm rms.

This results of this test conclusively demonstrate that the assumptions and techniques used for the design and analysis of the CGH test plate are valid. This proof of the concept strongly indicates that the method will work for secondary mirrors. We are currently pursuing the next step in the development of the CGH test plate method -- using a CGH test plate to perform a full-aperture test on a 10-inch secondary mirror.