CGH Report Guide

Diffraction International designs and analyzes aspheric null tests using OSLO SIX optical design software. This software was selected because it can be programmed to automate much of the design and documentation process and has few hard limits on array sizes, etc. Much of the design documentation is generated by standard OSLO commands and proprietary OSLO CCL programs. CGH encoding and digitization are performed using Diffraction International's proprietary HoloMask software. Both OSLO and HoloMask can generate AutoCAD compatible graphic data.


SUMMARY

DESIGN

ANALYSIS

VERIFICATION AND CERTIFICATION

ELECTRONIC APPENDICES


SUMMARY

Certificate of Compliance

This certifies that the CGH null meets all specifications of your purchase order and associated documentation as well as Diffraction International's own specifications. Any exceptions are noted.

Instructions for Use

These customized instructions should enable anyone experienced in interferometry to use the CGH null to perform an aspheric null test.

Test configuration diagram

This oblique view shows the null test configuration with the CGH on the left and the test beam propagating to the right. The CGH coordinate axes and frame orientation are shown. If the scale is such that these are difficult to see, then this information is repeated in an enlarged view at the upper left of the drawing.

CGH aperture layout

These diagrams show the apertures of the CGH null and the Alignment CGH (if any). The null aperture is the actual CGH null. A "retro" aperture diffracts the test wavefront back on itself to create a null interferogram and serves as an aid in aligning the CGH. HA50 Series Alignment CGHs consist entirely of retro apertures with the relevant ones shaded. An "autocollimation" aperture produces a collimated wavefront, usually perpendicular to some planar feature on the test optic. It is used to align the test optic tilt and tip independent of the centration and focus. A "vertex" aperture focuses light onto the test optic vertex to serve as a coarse centration aid.

Box label

The box label is provided as an aid in identifying the correct CGH null. With experience, the information on the label is sufficient for positioning the CGH relative to the interferometer.


DESIGN

Double-pass raytrace model

This is a partial tabulation of the OSLO double pass raytrace model; the complete lens file is included as an electronic appendix. The raytrace model begins and ends with a focused or collimated wavefront. The CGH is modeled as two superimposed surfaces labeled CGH Carrier and CGH Phase. The interferometer optics are not modeled. This listing concludes with a tabulation of vertex coordinates with respect to the CGH face and with respect to the test optic.

Aspheric departure and beam footprint diagram

This four quadrant diagram summarizes the null test geometry. The upper left quadrant shows the asphere departure in test wavelengths (usually 632.82 nm) from a "best fit" sphere, versus radial coordinate in lens units. The best fit sphere is here defined as matching the asphere at the vertex and edge. A dashed curve represents spherical extrapolation of the asphere vertex radius. A dashed vertical line, when present, indicates the clear aperture limit.

The upper right quadrant shows the null test configuration beginning on the left with a wavefront perpendicular to the return surface (usually the asphere) and ending with a spherical or collimated wavefront after the CGH. The P-V and RMS design residuals are reported. The interferometer optics are not shown.

The lower left quadrant shows a square grid representing the design aperture footprint on the test optic. Any grid points which appear as red X's are vignetted later in the raytrace, such as by an undersized CGH.

The lower right quadrant shows the design aperture footprint on the CGH and the shape of the CGH fringe pattern. Each plotted fringe represents several actual fringes (or line pairs) as noted. Also given are the F/# and location relative to the CGH of the spherical or plano test wavefront. If a negative value is given for Z0, then the CGH is in a converging spherical wavefront. The polynomial degree of the CGH phase function is noted.

Asphere sag table

The asphere sag table is generated by the OSLO software. It serves as a check on whether we have properly modeled your asphere. We will choose the aperture increments to match any sag table supplied with the asphere specification.

CGH phase table

The CGH phase table is generated by the OSLO software. The CGH fringes are contours of equal phase and one unit of phase represents one fringe. Our sign convention follows a thin lens analogy in that diffracted light is bent toward regions of higher phase value.


ANALYSIS

Pupil mapping analysis (table and equations)

The pupil mapping table traces a grid or fan of rays from the test pupil to the test optic surface, to the CGH face, and then on to the spherical or collimated source.

In the case of a spherical source, ray coordinates after the CGH are specified by their direction cosines. Direction cosines are accurately scalable to image coordinates, assuming your interferometer has well-corrected imaging optics and the interferometer axis is correctly aimed (usually perpendicular to CGH face).

The pupil mapping table also given in the form of polynomial equations that transform between test optic coordinates, CGH coordinates, and exit pupil direction cosines. There are usually six sets of transformation equations. The most useful of these are CGH-to-image, asphere-to-image and image-to-asphere. Our Durango Interferometry Software fully supports pupil mapping through its morphing feature.

Ghost diffraction analysis (diagram and table)

The ghost diffraction analysis consists of a 4-panel diagram and an associated table. The visibility of ghosts (and also the test wavefront) depends on the diffraction efficiencies of the CGH, the reflectivity of the test optic, and the field of view (FOV) of your interferometer.

The ghost analysis will generally assume that your interferometer has a FOV of ±500 tilt fringes. The actual angular FOV can be determined by testing a flat mirror and noting how much tilt is required to cause the interferogram to go dark-the interferometer's full angular FOV is equal to the maximum mirror tilt. Zoom position may affect your interferometer's FOV. For spherical test wavefronts, the linear FOV is equal to the angular field of view (in radians) multiplied by the focal length of the Fizeau sphere or equivalent accessory optic. If the CGH is located in a diverging spherical test wavefront, you can reduce the FOV by placing an aperture flag at the focus. This will be noted in the Instructions for Use.

If the test wavefront converges to a real focus between the CGH and the test optic, then the upper left panel shows a spot diagram of the various diffraction orders at this focal plane as seen from the interferometer side. The zero order diffraction is black, marked by a "+" symbol, and will remain if the CGH is removed. The desired first order diffraction is green and other diffraction orders are red. A black circle represents the recommended pinhole spatial filter size and location to pass the green first order wavefront.

Otherwise, the upper left panel is a raytrace of the various ghosts resulting from three incident rays at fractional pupil coordinates 0.0 and (0.7. The interferometer is not shown but would be located to the right. The test wavefront rays are shown in green, transmitted ghosts are red, and reflected ghosts are blue.

The upper right panel shows a spot diagram of the various diffraction orders as they appear (or would appear) at the cat's eye focus of the interferometer. This diagram can be useful when aligning the test optic to select the correct diffraction order. In the case of a convex test optic or afocal configuration, the focus is virtual or at infinity but may be observed by placing the interferometer into alignment mode. Black dots represent the zero order transmitted ghost which remains (and gets brighter) if the CGH is removed. Other ghosts transmitted by the CGH are represented by red dots. Ghosts reflected by the CGH are represented by blue dots. A black circle indicates the field of view specified for the ghost analysis. The focal plane diagram is plotted using CGH coordinates, therefore the FOV circle is decentered for off-axis CGH nulls. The test wavefront is perfectly focused and would appear as a single dot in the center of the FOV circle, so it is instead represented by a green '+' symbol.

The lower left panel shows a spot diagram pupil map of the test wavefront as it returns through the CGH. The density of dots is linearly scaled to represent intensity with 100,000 dots over the full circular pupil corresponding to full intensity of the test beam.

The lower right panel shows a spot diagram pupil map of CGH diffraction ghosts. Only rays within the specified FOV circle are plotted. The dot density again represents intensity and can be graphically compared to the test wavefront intensity. Red dots represent ghost rays which are transmitted by the CGH and diffracted (wrongly) once or twice. These ghosts can be blocked (temporarily) by inserting a card immediately after the CGH. Black dots represent the zero order transmission ghost which remains when the CGH is removed. Blue dots represent rays which are reflected by the CGH. These rays will remain even if the test optic is blocked.

A table lists each combination of diffraction orders which can propagate through the CGH, to the test optic and back through the CGH to the interferometer. First order diffraction, highlighted by an arrow, is the test wavefront of interest. It has nominally zero tilt or residual aberration. All other combinations of diffraction orders are unwanted ghosts which must be sufficiently tilted, aberrated or vignetted to prevent their being viewed in the interferogram.

The columns labeled "Out" and "Back" represent the diffraction orders for each pass through the CGH. Subsequent columns report the wavefront residual and tilt for this combination of diffraction orders. The column labeled "%inFOV" indicates the fraction of the test or ghost beam which returns unvignetted through the CGH and within the assumed FOV. Ghost beams may be vignetted by the interferometer optics or by an aperture flag at the cat's eye focus. Note that improper test optic alignment can sometimes cause a ghost beam to be nearly nulled and the test beam to be tilted and aberrated.

The column labeled "Return" represents the fraction of the outgoing test wavefront intensity returned to the interferometer through this diffraction channel, based on theoretical or measured values of the CGH diffraction efficiency and test optic reflectivity. Usually, a test wavefront return of 0.035 is desired to match an uncoated Fizeau reference surface reflectivity of 0.035. Note that, in the case of a chrome type CGH, the first order test beam does not have the strongest return. The spot diagrams are a better indicator of visibility since the ghosts are generally not well focused.

Generally, the ghosts corresponding to diffraction order combinations −1,+3 and +3,−1 are the most troublesome. They can interfere with each other to form low spatial frequency fringes even if tilted significantly with respect to the test beam. The other "2-sum" ghosts corresponding to diffraction order combinations 0,2 and 2,0 are less visible because of their lower diffraction efficiencies, particularly in the case of phase gratings.

Following the transmission ghosts is a listing of reflection ghosts corresponding to diffraction orders which reflect off the CGH and back into the interferometer. This are usually negligible for phase type CGHs.

Diffraction International attempts to eliminate all significant ghosts from the test configuration by manipulating the CGH location and CGH carrier, and by recommending the use of aperture flags and/or phase type CGHs where appropriate. Nonetheless, every interferometer and asphere null test configuration is unique and we continue to learn from experience. If you encounter a problem with ghosts, please let us know and we will work with you to resolve it. If the interferometer field of view and test optic reflectivity used for the ghost analysis do not accurately represent your configuration, we will gladly repeat the analysis.

Sensitivity analysis (table and synthetic interferograms)

The double pass sensitivity analysis is generated by Diffraction International's proprietary OSLO CCL software. The documentation begins with a listing of the lens surfaces for identification purposes. The surface numbering will be different than for the single pass model. A notation "GC 1" in the tilt/decenter data indicates that the surface is specified in global coordinates relative to surface 1¾usually the CGH face. The list of variables defines compensators; these typically consist of the focus, decentration and tilt of the test optic (usually expressed relative to the CGH). The variables follow OLSO notation.

The interferogram P-V and RMS are determined by tracing a dense bundle of rays (typically >7500) to the cat's eye focus position or, in the case of an afocal system, to the CGH face. Relevant design parameters are perturbed one at a time, the compensators are varied to minimize the RMS wavefront error while maintaining zero tilt fringes, and the residual P-V and RMS wavefront error and the required compensator values are reported. If the optimization would cause a compensator value to violate imposed limits, then its value is reported as MIN or MAX.

When a compensator is perturbed, it is temporarily removed from the null optimization.

Retrace errors can occur if the interferometer test wavefront departs from its spherical or collimated ideal or if the test wavefront is not concentric with the Fizeau sphere or parallel to the Fizeau flat. Sensitivity to retrace errors can be determined by including the Fizeau reference surface in the model, then adding Zernike phase perturbations to the wavefront at the first encounter with the Fizeau surface and then removing identical perturbations on the return pass.

Transmitted wavefront distortion of a Fizeau interferometer and accessory optics is commonly a fringe or more for a fast Fizeau sphere. If the test configuration shows sensitivity to wavefront tilt (Zernikes #1 and #2), then, rather than relying on alignment mode, it is better to check Fizeau sphere tilt and tip in cat's eye configuration or Fizeau flat tilt and tip against a corner cube reflector. If the test configuration shows sensitivity to wavefront power (Zernike #3), then interferometer collimation can be checked with a shear plate and, if the interferometer is properly collimated, Fizeau sphere concentricity error can be tested in transmission against a Fizeau flat.

Alignment of the interferometer relative to the test configuration is modeled by varying the location of the point or collimated source. For focal configurations there are three degrees of freedom corresponding to the X,Y,Z location of the cat's eye focus. For afocal configurations the degrees of freedom are tilt and tip, expressed as interferogram fringes over the frame aperture.

CGH substrate meniscus is expressed in fringes over the frame aperture. CGH substrate power and wedge are expressed in fringes over the clear aperture.

One parameter, CGH pattern distortion, is treated differently because it cannot be readily modeled. The CGH aperture is uniformly sampled and the effect of a localized 1 micron error in pattern placement is computed based on the local grating spatial frequency. These samples are combined statistically to yield P-V and RMS wavefront errors.

Synthetic interferograms supplement the printed sensitivity analysis. For each perturbed parameter for which the residual wavefront error is large enough to yield an informative plot, a synthetic residual interferogram is plotted. A label at the top of each synthetic interferogram gives the parameter name, design value and perturbation increment. These exactly match columns 1 through 3 of the sensitivity analysis. The synthetic interferograms can be of considerable use in understanding and nulling observed interferograms.

Tolerance analysis

The tolerance analysis is derived primarily from the sensitivity analysis which is summarized in columns 5 through 7. The reference surface is generally assigned a tolerance of 0.1 wave if spherical or 0.05 waves if plano. Design parameters of the test optic are assigned a tolerance value of zero unless explicit tolerances have been defined in the specification. The P-V Percent column gives the relative contribution of each tolerance value to the overall test accuracy. The Notes column explains various tolerance values.


VERIFICATION AND CERTIFICATION

A publication by Arnold and Kestner, "Verification and Certification of CGH Aspheric Nulls", SPIE Vol. 2536, 117-126 (1995), describes verification and certification methods in some detail. Reprints are available from Diffraction International.

Nikon verification of registration

The aperture locations of Nikon marks embedded in the CGH data and listed in the log file are measured by our photomask vendor and compared against design locations to verify the accuracy of the e-beam writing process. The Nikon report lists the X and Y deviations of each measurement point from the design locations.

Substrate interferograms before patterning

To assure wavefront quality, we obtain transmission interferograms of our precision AR coated CGH substrates prior to chrome coating and patterning. For e-beam masters on photomask quality substrates, transmission interferograms before patterning are not available, transmitted wavefront is not specified by the manufacturer, and we must accept what we get.

Whenever tilt, power or reference are subtracted from an interferogram, this will be so indicated. Reference here refers to an empty cavity interferogram obtained before (or after) insertion of the CGH. By subtracting this reference, we obtain an absolute measure of the CGH substrate transmitted wavefront distortion, including wedge.

Zero-order interferograms before phase etch

We obtain zero order interferograms after patterning so that measured substrate aberrations can be registered to the clear aperture. We try to use a sufficiently long test cavity to walk any non-zero orders off the aperture, but for some CGHs this is not practical and the interferogram will contain transmitted or reflected diffraction ghosts over some portion of the aperture. In other respects, interferograms before and after patterning should agree since the transmitted wavefront distortion is unaffected by patterning. For chrome type CGHs, zero order transmission interferograms can be verified by the end user.

Zero-order interferograms after phase etch

For phase type CGHs, there is nominally no zero order and the transmitted wavefront distortion cannot be measured in the usual manner. Diffraction International therefore obtains transmission interferograms of phase etched CGHs with the chrome etch mask still in place. The effective substrate transmitted wavefront distortion (for any but zero order diffraction) is the average of this interferogram and one obtained prior to phase etching. If the phase etched and chrome masked interferogram cannot be obtained because of diffraction ghosts, we will estimate the transmitted wavefront distortion from the unpatterned substrate interferogram and an assumed etch depth uniformity.

When a fiducialized interferogram of the patterned substrate prior to phase etch is available, we will average this with the post phase etch interferogram to best represent the effective wavefront distortion. We may also subtract the pre phase etch interferogram from the post phase etch interferogram to obtain a measurement of the etch depth uniformity.

Framing certification

Diffraction International measures the location and orientation of each CGH in its frame using an alignment fixture. Frame alignment is important only if it must be transferred from one CGH to another (e.g. HA50 Series Alignment CGH to custom CGH null). The reported decenters and tilts follow the OSLO notation and are defined in the coordinate diagram which follows. The plane of the CGH face relative to the frame balls is measured in an absolute sense. Alignment in the plane of the CGH is relative to the alignment fixture and includes a small bias error common to all CGHs.

The user can verify relative framing errors with ordinary metrology tools commonly available in the optics lab. The CGH should be oriented to contact the CGH mount using the three tooling balls nearest the key notch. Relative TLA and TLB are easily measured using your interferometer or an autocollimator to observe zero order reflection off the CGH face. Relative DCZ can be measured with a dial gauge contacting the center of the CGH face. Absolute TLA, TLB and DCZ can be measured similarly by resting the CGH face up on a surface plate. Verification of DCX, DCY and TLC require viewing of the CGH fiducial marks. For Model 50R and Model 50 frames, these are located at the four corners of a 30 mm square centered on the CGH. We use the two marks along the lower edge of the frame. Use a microscope with crosshair to focus on a fiducial mark and then replace the CGH, noting the apparent change in location of the fiducial mark. Repeat for the second fiducial mark. Placing the CGH face up on an abrasive surface might wear flats on the frame balls, affecting the measured values of TLA, TLB and DCZ relative to a reference flat. Such wear will not degrade performance since these wear points are not the points which contact the CGH kinematic mount.


ELECTRONIC APPENDICES (CDROM)

OSLO lens files (filename.osl and filename.dbl.osl)

Null tests are designed in single pass starting at the return surface (usually the asphere) and ending with a focused or collimated wavefront. To create a wavefront perpendicular to the return surface, the medium preceding this surface is assigned a refractive index of 1E-20. The CGH is modeled as two superimposed surfaces. The "CGH Phase" surface is a polynomial diffractive surface. The "CGH Carrier" surface is an HOE type surface, as produced by recording the interference of two point sources. Source 2 represents the spherical or collimated wavefront from the interferometer whereas Source 1 represents the diffracted carrier. Boundary drawing information is included to indicate the orientation of the CGH frame. OSLO can model any type of aperture using Boolean combinations of simple apertures. The CGH aperture is placed on the "CGH Phase" surface and modeled as the intersection of a circle or ellipse and a rectangle.

The double pass file is constructed automatically from the single pass file using a proprietary .CCL program. The double pass file uses global coordinates and pickups to tie the return surfaces to the outbound surface. Surface 1 is usually the CGH Face, so global coordinates are the same as CGH coordinates. The field point which we have defined corresponds to the real or virtual cat's eye focus location or, in the case of afocal configurations, the direction from which a collimated test wavefront is incident. Because we use a right handed coordinate system with x to the right and y at the top as seen from the interferometer, the double pass model is "strange" with outbound rays propagating along the negative z axis. Consequently, diffraction orders are inverted compared to the single pass model.

ZEMAX lens files (filename.zmx and filename.dbl.zmx)

These files are translated from the OSLO lens files by a proprietary .CCL program. Some features, particularly complex apertures, may not translate correctly, resulting in bad wavefront statistics due to rays which should have been blocked. Also, Focus Software has only recently released some upgrades to ZEMAX which allow it to handle a larger number of polynomial coefficients and to properly treat the zero index initial medium in the case of decentered pupils. If this file generates errors, make sure you are using the most recent version of ZEMAX.

CODE V lens sequence files (filename.seq and filename.dbl.seq)

These files are translated from the OSLO lens files by a proprietary .CCL program. The sequence file also draws the lens and executes a wavefront analysis. Some features, particularly complex apertures, may not translate correctly. Other limitations of CODE V may prevent translation of one or both files. In particular, CODE V does not support the near zero index medium which we use in modeling all single pass, center of curvature tests. Also, CODE V is unable to handle more than a 10th order phase polynomial on non-rotational HOE surfaces, a 20th order polynomial on rotational HOE surfaces, or long file names. If an interferogram file (.INT) is used to describe the CGH phase function, then the absolute pathname to this file will be specified in the .seq file and you will need to edit it to match your directory structure.

AutoCAD DXF double-pass lens file (filename.dbl.dxf)

This is the OSLO double pass lens file as exported by the OSLO "dxf_lens_drawing" command. The CGH frame boundary drawing information is included to indicate the frame orientation. Circular arcs are approximated by piecewise linear polylines.

HoloMask log files (*.log)

These log files are produced by Diffraction International's HoloMask and related software used to encode and digitize the CGH pattern. The log files begin with parameters defining the CGH phase function and aperture. These parameters are exported from OSLO and should exactly match equivalent parameters of the OSLO lens file. HoloMask log files may include a CGH phase table matching that generated by OSLO. HoloMask will list the magnitude and aperture location of any and all encoding errors which, upon digitization, could possibly exceed thresholds specified by the encoding parameters. A list of encoding errors does not signify a problem unless the reported magnitudes are unacceptable. The DXB to MEBES conversion log file lists the aperture locations of fiducial marks used to align the CGH and of Nikon marks used to verify the registration accuracy of the e-beam writing. Finally, a MEBES to AutoCAD DXB conversion utility extracts a list of fringe edges and optionally generates test plots.

EdgeChk verification of encoding and digitization (*.log)

The list of fringe edges extracted from the digitized MEBES data is compared against the computed phase values at sampled points on those edges to verify the accuracy of the encoding and digitization process. Aperture sample points are grouped into rectangular cells of a size approximating one pixel of the interferometer camera. Statistics are reported by sample point and by sample group. The point sample statistics are appropriate for an infinite spatial resolution interferogram whereas the group sample statistics are appropriate for a video resolution interferogram.

Tolerance analysis spreadsheet (jobnumber.xls)

This EXCEL file is an electronic version of the printed tolerance analysis. Use it to do your own what-if analyses.

Durango interferogram data files (*.opd)

These are the electronic interferogram data files from which the printed interferogram documentation was derived.