Absolute planarity measurements by interferometry are classically made using three flats, compared two by two in the course of four or more tests. Data reduction is performed with various analytical methods. Here we present instead a data processing algorithm that converges to solution numerically by iteration. Examples are presented both on synthetic interferograms and on experimental data. High accuracy and versatility of the approach are demonstrated.

Iterative algorithm for three flat test

Fritz’s method [Opt. Eng.23, 379 (1984)] of
using Zernike polynomials to assess the absolute planarity of test
plates is revisited. A refinement is described that takes into
account the data decorrelation that appears in experiments. An
uncertainty balance is defined by propagation of error contributions
through the steps of the method. The resultant measuring procedure
is demonstrated on a data set from experiments, and a nanometer level
of uncertainty is achieved.

Absolute measurement of planarity with Fritz's method: uncertainty evaluation.

Measuring flats in the horizontal posture with interferometers is analyzed in detail, taking into account the sag produced by gravity. A mathematical expression of the bending is provided for a plate supported at three unevenly spaced locations along the edge. It is shown that the azimuthal terms of the deformation can be recovered from a three-flat measuring procedure, while the pure radial terms can only be estimated. The effectiveness of the iterative algorithm for data processing is also demonstrated. Experimental comparison on a set of three flats in horizontal and upright posture is provided.

Three-flat test with plates in horizontal posture

To determine the absolute flatness deviations of optical surfaces, a novel method using two optical plates to achieve the absolute flatness test is presented. Absolute deviations of three surfaces, the rear surface of plate I and the front and rear surfaces of plate II, are obtained by four measurements. Wavefront error due to the inhomogeneity of plate II is measured beforehand and is then subtracted from the test results. Vertical profiles of the three surfaces are compared with the measurement results obtained by Zygo's three-flat application. Good agreement validates our method. The advantage of our method is that only one transmission flat is needed during the absolute test, which is especially useful for large-aperture interferometer calibration.

Method for absolute flatness measurement of optical surfaces

The use of a simplified version of the liquid mirror approach to validate absolute planarity reference flats is described in detail. It is shown that the approach can serve the purpose, providing a measurement of the peak-to-valley departure from planarity that in experiments is within 7 nm uncertainty (2σ) over a diameter of 90 mm.

Validation of absolute planarity reference plates with a liquid mirror

A large-aperture high-accuracy phase-shifting digital flat interferometer that is a combination of optics, mechanics, electricity, and algorithm is described. The aperture size is 250 mm and a liquid surface is used as an absolute flat to eliminate system error. The accuracy is better than ?/50 (?50.6328 µm, peak-to-valley value). The tested aperture can be enlarged to 500 mm. This interferometer has been used as an optical flat standard instrument for China. The optical interferometer, phase shifter, and calibration of precision are described.

Large‐aperture high‐accuracy phase‐shifting digital flat interferometer

Phase shifting interferometry (PSI) is a highly efficient and accurate phase measuring method. The accuracy of PSI is most seriously impaired by calibration error and nonlinearity in the phase shifter. This paper presents a new algorithm, the overlapping averaging 4-frame (OAF) algorithm, which can reduce the phase error due to phase shifter errors. The relationship between the accuracy of OAF algorithm and phase shifter errors is given. From this relationship, it is verified that the OAF algorithm can reduce the phase error due to phase shifter errors. The computer simulation providing the magnitude of a calibration error and nonlinearity in the phase shifter are shown for a number of different phase-measurement algorithms. From the analysis, the result is obtained that the OAF algorithm is more highly accurate than other phase-measurement algorithms.

New algorithm on phase-shifting interferometry: the overlapping averaging 4-frame algorithm

Today, high quantities lens is more and more important to the optic-electric fields, and it brought about the demand of high accuracy testing of spherical surfaces. Absolute interferometric testing of spherical surfaces is a technical basis for establishing the spherical standard, and it is also an important application of computer aid interferometry. Partly work in the course of establishing the national spherical standard is introduced. A new method based on image processing has been developed instead of typical absolute testing which requires an eight-dimension mount whose cost is expensive and adjustment is very difficult. Interferograms sampled by phase-shifting interferometry can be processed to recognize the border of spherical surfaces. The key coefficients of position are in real time feedback to the operator to adjusting sphere precisely relative to the interferometer. This method can get more accuracy because of the high unison of three interferograms. This paper shows results of testing a 1/10 wave P-V sphere using two aplanats. It is easy to measure spherical surfaces to the accuracy better than 1/15 wave p- v.

Realization of spherical absolute testing

This paper describes a large-aperture high-accuracy phase-shifting digital flat interferometer which is a combination of optic, mechanics, electricity, and algorithm. The aperture size is 250 mm and liquid surface is used as an absolute flat to eliminate systemic error. The accuracy is better than (lambda) /50 ((lambda) is Hz-Ne laser wavelength) (peak-to-valley value). The tested aperture can be enlarged to 500 mm. This interferometer will be used as our country optical flat standard instrument. This paper describes the optical interferometer, phase shifter, and calibration of precision.

Qingyun Wang

Papers

Large‐aperture high‐accuracy phase‐shifting digital flat interferometer

New algorithm on phase-shifting interferometry: the overlapping averaging 4-frame algorithm

Realization of spherical absolute testing

Large-aperture high-accuracy phase-shifting digital flat interferometer

Precise Real-time Navigation of the Small TJU-1 Satellite Using GPS, GLONASS and BDS