Debunking a common metrology myth: Pixel Scale ≠ Resolution!
Debunking a common metrology myth: Pixel Scale ≠ Resolution!
As optical surface specifications on the power-spectral density (PSD) and local slope become more commonplace, Fizeau interferometers are being used to measure mid-spatial frequency errors on the surface in addition to traditional global figure errors. Measuring smaller feature sizes requires careful consideration of the measurement system. While the Nyquist limit states that features with a period as small as two pixels can be measured, this does not mean that such features are measured with high-fidelity. Instead, features near the Nyquist limit often have their amplitudes greatly reduced by the measurement device. Therefore, it is desirable for the measurement system’s Nyquist limit to be much lower than the smallest feature that must be accurately measured. However, it is often not possible to satisfy this constraint and obtain a full aperture measurement of the sphere or asphere under test.
Stitching with an SSI-A® or ASI® solves this problem using the magnification inherently gained by subaperture stitching. Smaller feature sizes can be accurately resolved while at the same time giving a full aperture measurement of the surface and increasing the lateral dynamic range of the instrument.
The figures below demonstrate some of the key benefits of stitching: higher “real” resolution and increased lateral dynamic range. In Figure 1 and Figure 2, compare the detail in the 1 mm sections of the full aperture measurements and the relative amplitude of the integrated PSD plots – a high extension factor stitched measurement clearly gives the most accurate measurements of fine, high-frequency features. In Figure 3, the CGH and SSI-A measurements contain the same number of pixels, but the stitched measurement reveals much finer structure. For more information, see [Murphy & Youngworth, Optifab 2009], [Supranowitz et al., ASPE 2010], and the APS article elsewhere in this newsletter.
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Figure 1 – Three measurements of the same part with different transmission spheres. The high extension factor stitched measurement shows much finer structure than the full aperture test. |
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Figure 2 – PSD plot for three measurements of the same part. The smallest feature that full aperture test can accurately measure is 250 microns, roughly three times larger than the cutoff predicted from the Nyquist limit. The f/3.3 stitched measurement can accurately measure features as small as 50 microns – a 5X improvement over the full aperture test. |
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Figure 3 – A CGH measurement (left) and a stitched measurement with the SSI-A (right). Each measurement contains 500 x 500 pixels, but the stitched measurement contains much more high frequency information. The number of pixels is not an indication of the smallest measurable feature! |
