ZYGO干涉仪2

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Copyright Zeeko Limited,2008,Zeeko Stitching Interferometry,Commercial in Confidence,Why use stitching interferometry,Extend the aperture of an interferometer measure larger diameter parts,Enable measurements on high-NA convex parts,Can be used to extend the aspheric measuring range of an interferometer,Can be used to give increased spatial resolution,Can shorten the optical length of the interferometer cavity to reduce the effects of turbulence,Commercial in Confidence,Measuring Instruments,We measure the surfaces with respect to an optically or mechanically defined datum.,Profilometric techniques.,Optical(Interferometric)techniques.,I will concentrate on interferometry,Recipe for Stitching,We seek to join together several overlapping measurements of parts of a surface.,We need to minimize the discrepancy in the overlap areas,a minimization problem.,We must somehow transform the data in each measurement in a way that makes it fit the other measurements,without altering the overall form information in the data,We start by visualising the measurement process.,An example using a convex surface under test,We have a sub-aperture map on the surface to test,We then have a series of sub-apertures after the measurement,Summary of the stitching process,Measure first sub-aperture,Move to next position,Measure next sub-aperture,All done?,No,Yes,Generate a guess transformation for each sub-aperture,Transform sub-apertures,Compute merit function,Merit function low enough?,Generate better guess,Form a new data set with all points,Filter data set,Use it!,Yes,No,Transformations,We must apply transformations to the data to stitch the measurement sets.,Use a matrix formalism we express the transformations required in a single matrix and use this in a least-squares optimization.,We have a point cloud of data for each measurement result:,Transformations(cont),We apply a transformation matrix to the points to give the new points,Only certain operations are allowed:,Linear translation,Polar rotation,Aberration correction,Tip,tilt,defocus,distortion and reference surface subtraction,A transformation looks like(excluding defocus):,A and B are the tip and tilt(shearing),(t,x,t,y,t,z,)are the linear translation components and,is the polar rotation angle.,Adding defocus terms is more involved and involves computing a defocus coefficient for each data set difficult with non-circular apertures,and generally computationally intensive.,Measure first sub-aperture,Move to next position,Measure next sub-aperture,All done?,No,Yes,Generate a guess transformation for each sub-aperture,Transform sub-apertures,Compute merit function,Merit function low enough?,Generate better guess,Form a new data set with all points,Filter data set,Use it!,Yes,No,Summary of the stitching process,Interferometer Imaging Distortion,OBJECT,BARREL,PINCUSHION,DISTORTED IMAGE,Interferometer Imaging Distortion,OBJECT,BARREL,PINCUSHION,DISTORTED IMAGE,Data manipulation,The acquired phasemaps are then corrected for,Residual aberrations(calibration of the reference wavefront,Scale(using base radius from cats eye),We are also working on reverse ray-tracing for more aspheric parts computing the interferograms that result from aspheric parts to aid the data manipulation,Stitching,The stitching proceeds by optimization.,The phasemaps are transformed against a merit function that minimizes the distances between the fiducials,When the best minimum is found,the data are stitched.,The stitching error is estimated from a measurement of the residual noise,the merit function and an analysis of the data in the sub-aperture overlap areas,Commercial in Confidence,Some Example Data(full-aperture and stitched)to illustrate,Stitched 4 sub-apertures on a circular flat to compare a full-aperture measurement with the stitched result,Used an old Zygo PTI interferometer to show what can be achieved,AGC on camera(bad for phase shifting as gain varies between frames,especially near null testing),Old vidicon tube camera(NOT CCD)non-linear,no pixels to speak of,Poor optics compared to todays models,Numbers will be much better on modern interferometer,Commercial in Confidence,Full-aperture measurement,Commercial in Confidence,Raw sub-aperture measurements,Commercial in Confidence,Stitched sub-apertures(before combining),Commercial in Confidence,Stitched sub-apertures(&moderately filtered version),Commercial in Confidence,Comparison,And the difference,Full-aperture,Stitched,RMS,PV,Full-aperture,32.0 nm,204 nm,Stitched,29.2 nm,208 nm,Commercial in Confidence,Comparison:full-aperture-stitched,PV=92 nm(1/7 wave),RMS=11 nm(1/60 wave),Much of the residual error here is systematic and calibration would remove it leaving only a few nm,(each sub-aperture consisted of the average of 32 measurements),Zeeko expect residuals of the order of 1/100 wave PV after calibration X10 improvement,Unfortunat