Pseudo-Shear Interferometry (PSI) is a technique for obtaining enhanced, absolute accuracy in interferometric measurements. Whereas conventional interferometry yields measurements limited in accuracy by the optical system and by the reference surface, Pseudo-Shear Interferometry provides the capability for measurement accuracy which substantially surpasses it. The technique consists of a regimen for data taking and a mathematical procedure for analyzing the resulting data.
A family of three phase measurement techniques are described that are spatial analogs of the popular temporal phase-shift methods. For these spatial techniques, the need for an active element such as a piezoelectric translator or an electro-optic crystal is eliminated simply by adding tilt to the fringe pattern. Measurements are obtained over a uniform grid with an accuracy comparable to temporal phase-shift interferometry. Advantages and disadvantages are discussed.
Conventional phase measuring interferometry normally requires one-half to sixty seconds acquisition time, limiting measurement to stationary phenomenon such as optical element wavefronts. We have developed an instantaneous PMI that measures displacements at one point to a resolution of 0.003 microns. We will describe this instrument and an interferometer measuring phase to lambda/2000 with a measurement aperture of less than one microsec. Also described is an attached system for analysing and displaying wavefronts at up to 10 Hz.
A heterodyne, Mach-Zehnder interferometer system has been developed for testing the wavefront quality of laser diode collimator pens. The testing system is described and the problems associated with testing laser diodes are discussed.
To implement a semiconductor laser diode for use in high density optical data storage systems, the output laser beam must be first collimated and then focussed to a near diffraction-limited spot. Therefore, it is essential to know both the beam intensity profile and the phase distribution of the laser wavefront with high precision on the order of one fiftieth of a wavelength. This measurement is important to both the laser diode manufacturers and users. In this paper, we will describe how the wavefront of a laser diode collimator pen was measured by using a state-of-the-art phase measurement interferometer built by WYKO Optical, Inc. Performance of this interferometer is evaluated using both He-Ne and diode lasers.
This paper describes a method by which recorded moire interferograms of diffuse, non optical surfaces may be processed using the principle of optical phase measurement by AC interferometry. In this method, a moire interferogram is recorded and processed as a transparency. The resulting interferogram is equivalent to a low spatial frequency optical hologram. An optical wavefront whose phase variations can be reconstructed from a plane wavefront and interfered with a second coherent plane wavefront of slightly different optical frequency, resulting in an interferogram appropriate for measurement by temporal electronic phase measurement. The results compare favorably to direct contact measurements.
An optical surface microprofiling instrument is described in this paper. The instrument is an interferometric device capable of measuring the the microtopography of a precision surface along a single scan line. A 25 millimeter. scan can be accomplished in less than one minute with the present hardware. The vertical resolution of the instrument is on the order of 10 Angstrons. The lateral resolution is diffraction limited and corresponds to a few micrometers. Surface profile data are output in the form of analog voltages that can be readily digitized by a computer for further analysis, if necessary. The microprofiler is a compact unit that requires no elaborate vibration isolation. Since the test is non-contacting in nature it is a non-destructive test. The instrument can potentially generate surface profile data for large samples. Numerous techniques exist for measuring the microtopography of precision surfaces. A brief overview will highlight the characteristics of the commonly used methods. This discussion will set a background against which the performance of the surface microprofiling instrument can be compared. Examples of surface profile data produced by the instrument for a variety of samples will be presented.
An optical heterodyne profilometer breadboard as been developed and demonstrated with surface roughness measurement sensitivity to 0.1 Å. Optical and electronic common-mode rejection techniques were employed in the optical heterodyne precision phase measurement scheme to resolve the optical phase to one part in thirty thousand. Vibration-induced optical phase jitter in the system was nearly eliminated by these common-mode rejection techniques. This non-contact profilometer is capable of characterizing mirror surfaces not limited only to flat and/or highly reflective surfaces. Concaved surfaces such as the x-ray mirrors for the Advanced X-ray Astrophysical Facility (AXAF) may be characterized as well. Several mirror samples have been characterized with the optical heterodyne profil-ometer which include two x-ray mirror samples. Roughness measurement results on the x-ray mirror samples have been compared with those measured by other methods.
As the standards of quality of a product increase, so also does the importance of the roughness measurement of technical surfaces. In the near future the most important methods for on-line measurement will be those, that work on a non-tactile basis. In this report, a new optical method is presented and described from a more experimenta] point of view to emphasize the application-oriented development of this electro-optical measuring device. Beginning with some remarks on the more theoretical characteristics, experiment results will be presented that have been obtained from both standardized and technical surfaces. The results reveal the ability to measure surface roughness in the range of approximately Ra = 0,06-10 um.
Measurements of two refractive samples were made at 0.915 μm of the BRDF to angles as close as 3° from specular. The data fit a one-dimensional power spectrum using vector electromagnetic theory. The autocorrelation length and its error were estimated and from these a most probable value and upper bound of the BRDF at 1° from specular were determined.
This paper presents a rationale for the precision measurement and characterization of surface finish using Fourier techniques. It offers a precise definition of figure and finish errors in the frequency domain and discusses particular finish statistics of importance for optical surfaces: the finish power spectral density and the mean-square finish error. Problems involved in estimating these quantities from practical measurements are discussed and illustrated. The need for an expanded data base of spectral shapes is emphasized.
The operation of a differential scatterometer developed at Montana State University is briefly described. The scatterometer takes and stores data under computer control. Analysis routines allow calculation of the surface power spectral density function (PSD) for the cases of one dimensional surfaces [Z(x) - diamond turned surfaces for example] and isotropic two dimensional surfaces [Z(x,y) - polished surfaces for example]. In addition, the zero and second moments of the PSD may be taken to provide bandwidth limited values of the root mean square roughness [a] and the root mean square slope [m]. Results from several samples are used to check the vector perturbation theory [Church, et. al. 1975] used by the computer to relate the scatter distribution function to the PSD. These experiments take advantage of the fact that the surface - and hence its PSD - remain a constant function during the measurements. Variations in the incident angle and polarization are introduced and the resulting PSD's are calculated and compared. In another experiment, the min/max scatter angles (or conversely the min/max PSD spatial frequencies) are matched to those of a total integrated scatter (TIS) system. Integration over the light scatter data and the PSD allows direct comparison to the TIS and effective rms roughness obtained by the TIS system.
Methods for analyzing surface profile data in terms of the finish power spectral density and mean-square finish error are discussed. Results of a preliminary comparison between mechanical- and optical-stylus measurements of a set of precision-machined surfaces are presented. Excellent quantitative agreement is obtained, although certain features observed in the case of strongly periodic surfaces require further study.
Encircled energy is an important specifying parameter for large, high quality optical telescopes and is critically dependent on the spatial frequency distribution of surface errors. Errors of surprisingly small amplitude whose spatial frequencies lie between those of the classical pupil aberrations and defects associated with the microroughness regime (i.e., whose periods lie below a millimeter) have a profound effect on encircled energy performance. This is particularly true at short wavelengths. Occurrence of this type of defect (called mid-frequency error) becomes more likely with increased mirror size. Full aperture interferograms that provide wavefront information over the pupil can lead to grossly inadequate performance predictions. Accurate prediction and the desired level of performance can only be achieved by precise measurement and control of the mid-frequency errors. This paper describes the processes and instrumentation for measuring and controlling figure error in this critical frequency domain during the manufacture of a high quality large aspheric mirror. Measurements of surface defects at the 0.002 µm rms level in the spatial frequency range of 0.01 to 0.25 cycle per millimeter are illustrated. The design and certification of a subaperture interferometer system is described.
The properties of a circularly ruled grating are discussed for the case in which the rulings are unequally spaced. This type of grating, which combines power and aberration control with conical mapping, is shown to be a key element in the design of the null corrector arm for an interferometer. Examples of test configurations are given for a non-linear axicon, a Wolter type telescope segment, and a fast aspheric.
Described is a technique for accurately measuring the wavefront aberration of aspherical optical surfaces with a lateral shearing interferometer. A computer controlled interference phase measuring technique is employed, which provides greater accuracy and real time data analysis. Key elements of the present system are a lateral shearing interferometer with a prallel plate, a piezoelectric-driven mirror, an areal image detector, and a microcomputer system with a graphic display. The shearing interferometer gives a fringe pattern corresponding to the derivative of the wavefront, which is analyzed by the fringe scanning method. By integrating the drivative of the analyzed data, we have the wavefront aberration of the test optics over an aperture containing 32 x 32 element array. A rms accuracy of measurement is 1/32 wavelength is achieved on the evaluation of a f/4 aspherical mirror.
A digital heterodyne interferometer has been designed and constructed to operate at a wavelength of 3.8 μm. The instrument is intended for use in measuring wavefront figure error due to thickness variations in dielectric coatings applied to infrared optics. A 32 x 64 element PtSi infrared CCD detector array is used together with digital processing and graphics display on a desktop microcomputer. Preliminary results have shown a wavefront measurement repeatability of less than λ/50.
A method is described for measuring the orientation of small plane surfaces several tens of micrometers on a side with a resolution of several seconds of arc. A laser beam waist is located on the test surface which underfills the surface. The reflected beam is detected by a quadrant detector to determine the offset of the beam from its nominal position. This displacement determines the relative angular difference from a predetermined angular standard. Advantages of this method for precise angle determination are the ability to measure small surfaces, insensitivity to translations of the test piece, large test piece clearance for inaccessible surfaces, and compensation for laser drift.
Surface topography is a topic of relevant interest to science, technology and industry. The method of projected interference fringes is reconsidered in view of applications to non-optical surface microscopic topography. Completion of the analysis of the limitations of the technique is continued in discussing method implementation with computer image processing techniques. Shifting of the fringe pattern by phase modulation to eliminate interpretation ambiguities and the discontinuous observation of the surface is examined for automatization of profile evaluation. Amplitude modulation for pulsed illumination is introduced combined with synchronized video-recording to the metrology of transient events.
Interferogram analysis is discussed as a sampling problem using the concepts of Fourier analysis. The relative merits of random, raster, and uniform sampling of a wavefront are examined. A relationship between a global least squares fit and interpolation in the spatial domain and transfer functions in the frequency domain is described.
The knife edge testing of optics is well known to be a sensitive but subjective test of an optical system. This test has been successfully used to figure telescope mirrors to a high degree of perfection. The problem with this test was that it was difficult if not impossible to get useful numbers as to the magnitude of error in the optic under test. With the advent of solid-state memory, microcomputers, and video sensors, we are now able to collect the information required to quantify the data available from the knife edge trace. The key to the new knife edge bench is the use of solid-state memory to capture and store pupil data so that it can be processed by the microcomputer. The system being described uses Zernike polynomials to bridge the gap between the subjective test and the objective measure. The Zernike polynomials are used to develop coefficients from the knife position. These Zernike coefficients are then converted to wavefront by using straightforward matrix operations.
A set of functions is presented which is orthonormal over the surface of a cylinder. The functions are useful for describing surface errors on the types of near cylindrical optics found in X-ray and some extreme ultra violet systems. In addition, the functions provide a convenient means of using surface deformation data to separate rigid body motions (misalignments) from surface errors. The functions are harmonic in the azimuthal direction, and polynomial in the axial direction. In this paper, the functions are detailed in terms of the form of their corresponding surface errors. Also, some general relationships are given, which relate the surface errors defined by these functions to the resulting wavefront errors. These relationships depend explicitly on the nature of the wavefront incident on the optic. This paves the way for describing the wavefront in a metrology configuration in terms of the errors on the optic and the misalignments in the system. Finally, some parallels are drawn between the use of these functions for describing near cylindrical optics, and the use of Zernike polynomials for describing conventional optics.
Two procedures are presented that allow for unambiguous separation of misalignment from misfigure in off-axis asphere interferograms. In the first method the coma observed is used to locate the element, while in the second method the element is located by minimizing the observed mean-square wavefront error. With either procedure, the misalignment-induced aberrations can be calculated and subtracted from the interferogram so that only true misfigure remains.
The basic limitation upon the ability to fabricate a particular surface lies in the ability to accurately test it. Aspheric elements have always presented problems in this regard due to a general lack of test equipment with which to perform the qualification. Lateral shearing interferometry provides a solution for testing a large range of aspheric surfaces since this technique has the ability to decrease the sensitivity to wavefront aberrations. Data reduction can then be used to reconstruct the original wavefront. This Paper examines a data reduction approach and provides the mathematics required to complete the analysis. Also included are the results of a study evaluating the program's performance in the Presence of data input errors.
The Air Force Weapons Laboratory (AFWL) located at Albuquerque, NM has developed a digital heterodyne interferometer capable of real-time, closed loop analysis and control of adaptive optics. The device uses independent phase modulation of two orthogonal polarizations of an argon ion laser to produce a temporally phase modulated interferogram of the test object in a Twyman-Green interferometer. Differential phase detection under the control of a Data General minicomputer helps reconstruct the phase front without noise effects from amplitude modulation in the optical train. The system consists of the interferometer optics, phase detection circuitry, and the minicomputer, allowing for complete software control of the process. The software has been unified into a powerful package that performs automatic data acquisition, OPD reconstruction, and Zernike analysis of the resulting wavefront. The minicomputer has the capability to control external devices so that closed loop analysis and control is possible. New software under development will provide a framework of data acquisition, display, and storage packages which can be integrated with analysis and control packages customized to the user's needs. Preliminary measurements with the system show that it is noise limited by laser beam phase quality and vibration of the optics. Active measures are necessary to reduce the impact of these noise sources.