Large-aperture Interferometer Research Articles

Optical phase-shifting methods based on low coherence laser for large aperture Fizeau interferometer

PZT is commonly used as the phase shifter in interferometric systems with small apertures for decades. However, it becomes more difficult to be applied to the system with large aperture. In this paper, the phase shifting procedure is moved to the source module with a low coherence laser, which makes phase shifting independent of the large interference cavity. The path matching procedure based on intensity variation is introduced to compensate the path difference between the two arms. The experiments based on PZT and wavelength tuning methods are both carried out on a 600mm Fizeau interferometer for verification of the proposed method. The difference between the two results is 0.0015λ(PV). Besides, repeated experiments are performed, showing excellent repeatability and stability and the standard deviation of RMS is 0.0011λ via PZT method. The analysis of error sources is also performed, including the poor contrast and the nonlinearity of PZT. Both the experimental results and the error analysis verify the feasibility of the proposed method in large aperture interferometer.

High-precision spherical subaperture stitching interferometry based on digital holography

A novel subaperture stitching interferometry is proposed to measure the high-numerical-aperture sphericity for workshop testing, which combined digital holographic technology, subaperture stitching algorithm and systemic aberration calibration. Each subaperture is fleetly measured by the digital off-axis holography with a single shot so that the influence of measurement environment can be effectively reduced. The high-precision full aperture shape is obtained by stitching these subapertures, meanwhile, the subaperture alignment errors and the systemic aberration can be correctly compensated by the method of least-squares with the Zernike polynomial fitting. The approach is verified by testing three spherical surfaces, including a concave sphere, a convex sphere, and a hemisphere, in general environment. Moreover, the measurement results are compared with full aperture results by using a large aperture interferometer of Zygo and stitching result by using a subaperture stitching interferometer of QED. The results based on the proposed approach are consistent with the commercial interferometers. Specifically, the relative deviations of RMS are 0.009 λ and 0.02 λ for testing a concave and a convex spheres, and that is 0.011 λ for testing a hemisphere. Our method not only has the comparable measurement accuracy with the commercial interferometers but also is more robust, feasibility and inexpensive than other subaperture stitching interferometry. We provide an anti-interference way to test spherical surfaces in workshop environment.

The Requirements for the Calibration Conditions in Large-Aperture Fizeau Interferometers

The problems that arise during the calibration of the reference plates of large-aperture interferometers are discussed and the methods for solving them are presented. It is shown that the repeatability of shapes of the reference plates after their rearrangements can be provided by selecting the mechanism of their fixing in place. It is demonstrated that the temperature deformations of the reference-plate surfaces can be determined from a numerical model. These measures have made it possible to calibrate the reference plates of the 630-mm interferometer with an accuracy of λ/1000 RMS (λ = 632.8 nm).

600-mm aperture simultaneous phase-shifting Fizeau interferometer

In this study, a 600-mm aperture simultaneous phase-shifting Fizeau interferometer is presented. This interferometer has a special light source configuration produced by an arrangement of four identical point sources diffracted by a phase grating. With this configuration, the phase shifts are introduced between each pair of coherent beams. A 2 × 2 image lens array is designed such that four conjugated interferograms with a phase step of π/2 can be captured in a single shot using one detector, thereby realizing dynamic measurement. The experiment was carried out using the proposed interferometer with a pair of 600 mm aperture transmission flat and reference flat placed on a platform with no vibration resistance facility. The results depict a peak-valley value of λ/10 and present a real-time phase variation caused by environmental factors, which indicates that the instantaneous measurement of the phase by the proposed large-aperture interferometer provides robust results despite the presence of environmental factors such as vibration and airflow.

Non-overlap subaperture interferometric testing for large optics

It has been shown that the number of subapertures and the amount of overlap has a significant influence on the stitching accuracy. In this paper, a non-overlap subaperture interferometric testing method (NOSAI) is proposed to inspect large optical components. This method would greatly reduce the number of subapertures and the influence of environmental interference while maintaining the accuracy of reconstruction. A general subaperture distribution pattern of NOSAI is also proposed for the large rectangle surface. The square Zernike polynomial is employed to fit such wavefront. The effect of the minimum fitting terms on the accuracy of NOSAI and the sensitivities of NOSAI to subaperture's alignment error, power systematic error, and random noise are discussed. Experimental results validate the feasibility and accuracy of the proposed NOSAI in comparison with wavefront obtained by a large aperture interferometer and stitching surface by multi-aperture overlap-scanning technique (MAOST).

Surface registration-based stitching of quasi-planar free-form wavefronts

Due to the lateral alignment incapability of planar subaperture stitching algorithms, subaperture testing (SAT) is still challenging especially for quasi-planar free-form wavefronts featured with vertical fluctuation of small amplitude and high frequency. To avoid the lateral misalignment-induced error, we propose a stitching algorithm with quasi-planar free-form surface registration. The subapertures are considered as three-dimensional point sets acquired from a free-form surface instead of the error surface superposed on a plane. Then all subapertures are stitched together by minimizing the deviations among overlaps with regard to the free-form surface. Finally cross-test simulations and experiments are presented to show the effect of error reductions in SAT of large continuous phase plate wavefronts, verified by the full-aperture testing with a large-aperture interferometer.

Polarization Fizeau interferometer based on birefringent thin film

A polarization Fizeau interferometer based on birefringent thin film is presented. The interferometer adopts a birefringent thin film to obtain orthogonally polarized and strictly common-path reference and test beams. Advantages include ease of implementation on large-aperture interferometer, measuring test optics from long distance, and achieving high fringe visibility. The phase shift is obtained by combining a quarterwave plate and an analyzer. The concepts illustrated are verified experimentally.

Deformation Analysis of Lateral Support of 600mm Aperture Interferometer Mirrors

The deformations of the 600mm aperture interferometer mirrors induced by gravity and supporting forces must be controlled strictly to ensure the accuracy of the large aperture interferometer to achieve 63nm. The mirror deformations induced by two types of forces and four axial distribution positions are analyzed respectively by finite element method. And the deformed interference wavefront are simulated by synthesizing deformations of reference flat and test flat mirrors. The maximum deformed interference wavefront formed by the cosine wave force at the middle of the mirrors and the minimum formed by the square wave force at the periphery of the mirrors. The peak to valley value varies 30nm and root mean square value varies 2.8nm between them. The measurement accuracy of large aperture interferometers can be improved by adjusting the force distributions and supporting positions of the mirrors according to the analysis.

Method for absolute flatness measurement of optical surfaces

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.

Field structures in nonlinear large-aperture cavity schemes with lens elements

An equation for the slowly varying envelope of a field in a large-aperture interferometer or a laser with intracavity lens elements is obtained using the quasi-optical approach and mean-field approximation. The case of a negative diffraction length of the cavity is analyzed. Ways for determining the transverse dimensions of dissipative spatial optical solitons in nonlinear interferometers and lasers are discussed.

Development of a line-scan CCD-based fringe tracker for optical interferometry

Traditional high-precision optical techniques, such as interferometry, are in ever-greater demand for noncontrolled environments. This is the case for the UPC-ZEBRA, a large-aperture interferometer that was built to measure vertical discontinuities (i.e., piston errors) in segmented mirrors. The large mechanical systems used to drive the interferometer to the different measurement positions generate perturbations that are highly incompatible with the expected piston measurements on the nanometer scale. We introduce a new system based on a line-scan CCD to track interference fringes. The error signal obtained from this fringe tracker has been used in a closed-loop control system to actively stabilize the interferometer. The perturbation has been attenuated by a factor of 1/200.

Effects of system apertures and defocus on the measured phase shift in interferometric displacement measurements

The difference between the phase shift occurring at the objectsurface owing to displacement and the phase shift occurring at theobservation plane of the imaging system of the interferometer isstudied. Analytical expressions for the phase shift for a number ofsurface displacements are found. From these expressions it is foundthat the difference between the phase shifts at the object and theobservation planes depends on the number of speckle-correlation modesin the observation plane and the product between the relative apertureand the relative defocus of the imaging system. For generaldisplacement the results indicate that the accuracy of a phase-shiftmeasurement with a small-aperture interferometer is limited only by thenumber of speckle-correlation modes at the observation plane for thecase of a focused system. For a large-aperture interferometer thephase shift at the observation plane becomes sensitive to defocusing ofthe imaging system. Agreement between theory and experiments is observed.

Automatic Fringe Analysis of Moiré Interferometry

The phase analysis of fringes by applying moiré techniques to the interferometer is well-known. Since this method is based on 2-D subtraction method in the incoherent optics, the distortion of the optical system is easily removed and a large aperture interferometer can be constructed. In this paper, a novel automatic method to detect phase of fringes was proposed by combining the conception of moiré-interferometer with a microcomputer system. The validity of the method is shown by experimental results in the phase analysis of fringes of slide-glasses. Furthermore, this system was applied to the measurement of pressure distributions in a Laval nozzle, and the measured results approximately coincided with the theoretical values. These results suggest that the system is well applicable to the fields of fluid mechanics.

Large aperture interferometer with phase-conjugate self-reference beam

A large aperture self-referencing interferometer consisting of a Twyman-Green interferometer using a self-pumped phase conjugator in series with test section optics is described and experimentally demonstrated. This interferometer provides twice the fringe shift of a Mach-Zehnder (M-Z) interferometer for a given optical phase change induced within the test section. It also provides greater irradiance in the reference beam than does a similar series setup utilizing a M-Z interferometer incorporating a local reference beam. Whereas the ordinary interferometer records instantaneous conditions, the new one records overage conditions if a BaTiO3 crystal is used as the phase conjugator.

Large-aperture interferometer with local reference beam

A large-aperture interferometer has been devised by adding a local reference-beam-generating interferometer to a schlieren system. Two versions of the interferometer were demonstrated, one employing 12.7-cm diam schlieren optics, the other employing 30.48-cm diam parabolic mirrors in an off-axis system. In the latter configuration, a cylindrical lens was introduced near the light source to correct for astigmatism. A zone plate was a satisfactory decollimating element in the reference-beam arm of the interferometer. Attempts to increase the flux and uniformity of irradiance in the reference beam by using a diffuser are discussed.

Large aperture interferometers with small beam dividers

This paper shows some practical intcrferometers for testing very large and very small specimens. This is accomplished by using a particular type of beam divider that operates near the vertex of a convergent or divergent beam of light that permits a lmost un limi ted size fields of view. Thus very large or ver.v s mall specimens ean be tested. Also, the wave front reversing propert ies of this beam divider permit tests to be made without the necessity of using standards of reference, thus eliminating the requirement for large standards that a re usually expens ive and require large working a reas . The principl es of these interferometers are so closely related to previously described instruments t hat very li tt le addit ion al explanation is required for an understanding of their operation. Several variations of the I\:oste rs pris m type of interferom eter a re s hown schcmaticall y J