A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques

We describe an imaging architecture for compressive video sensing termed programmable pixel compressive camera (P2C2). P2C2 allows us to capture fast phenomena at frame rates higher than the camera sensor. In P2C2, each pixel has an independent shutter that is modulated at a rate higher than the camera frame-rate. The observed intensity at a pixel is an integration of the incoming light modulated by its specific shutter. We propose a reconstruction algorithm that uses the data from P2C2 along with additional priors about videos to perform temporal super-resolution. We model the spatial redundancy of videos using sparse representations and the temporal redundancy using brightness constancy constraints inferred via optical flow. We show that by modeling such spatio-temporal redundancies in a video volume, one can faithfully recover the underlying high-speed video frames from the observed low speed coded video. The imaging architecture and the reconstruction algorithm allows us to achieve temporal super-resolution without loss in spatial resolution. We implement a prototype of P2C2 using an LCOS modulator and recover several videos at 200 fps using a 25 fps camera.

P2C2: Programmable pixel compressive camera for high speed imaging

In this paper, a novel accurate deformation distribution measurement technique by using sampling moire method is proposed. The basic principle and an experimental result of a steel beam in symmetric three-point bending are reported. In this method, the measurement area of a target is attached with an adhesive tape of a known pitch grating firstly. An ordinary CCD camera is installed on a fixed point to record the image during deformation. The captured image is analyzed by performing easy image processing, i.e., thinning-out and linear interpolation, to obtain the multiple phase-shifted moire patterns. Then, the phase distribution of the moire pattern can be calculated using phase-shifting method. Finally, the deformation distribution is calculated by the grating pitch times the phase difference of before deformation and after deformation. The experimental results in symmetric three-point bending test show that the displacement of the steel beam at loading point agree well with those obtained by an accurate displacement sensor. The average error of displacement measurement is less than 4 μm when 2 mm grating pitch is used, and it corresponds to 1/500 of the grating pitch accuracy. This indicates that noncontact deformation distribution measurement is possible by simple and easy procedure with high accuracy, high speed, and low cost for the structural evaluation of infrastructures.

Sampling Moiré Method for Accurate Small Deformation Distribution Measurement

The plenoptic function is a ray-based model for light that includes the colour spectrum as well as spatial, temporal and directional variation. Although digital light sensors have greatly evolved in the last years, one fundamental limitation remains: all standard CCD and CMOS sensors integrate over the dimensions of the plenoptic function as they convert photons into electrons; in the process, all visual information is irreversibly lost, except for a two-dimensional, spatially varying subset—the common photograph. In this state-of-the-art report, we review approaches that optically encode the dimensions of the plenoptic function transcending those captured by traditional photography and reconstruct the recorded information computationally.

Computational Plenoptic Imaging

A camera based on the digital micromirror device (DMD) technology has been previously developed. In this optical system, the correspondence of each mirror of the DMD to each pixel of the CCD cannot readily be done since the pixel sizes of the DMD and the CCD are very small. An accurate pixel-to-pixel correspondence adjustment in the DMD camera by means of the phase-shifting moire method is proposed. To perform high accurate adjustment of the optical system, the phase distribution of a moire fringe pattern is analyzed when the CCD pixels and the DMD mirrors have a mismatch and/or misalignment with each other. This technique does not need a complicated setting or complex image processing to generate the moire fringe pattern, and it needs only one captured image. In the adjustment experiment, the proposed method provided very accurate adjustment whose error was less than 1/25 pixel. An experiment of phase analysis to demonstrate the usefulness was performed.

Accurate pixel-to-pixel correspondence adjustment in a digital micromirror device camera by using the phase-shifting moiré method.

In phase-shifting digital holographic interferometry for measuring the displacement distribution of an object, holograms and reconstructed images have speckle noise, and they cause large errors in the calculation of the displacement analysis. In order to reduce the effect of speckle noise and hence to increase the sensitivity of the measurement of the displacement, we previously proposed a method using windowed holograms. In this paper, we propose a new method for averaging the obtained phase-difference values. Many phase-difference values at a point of the reconstructed image obtained with different windows for a hologram are averaged with weights. In order to check the effect on accuracy, the number n of windows used for averaging is varied. The weight, which is the m'th power of the absolute value of the complex amplitude of the reconstructed object, is also varied. As a result, when n becomes larger, the standard deviation of the errors becomes smaller. When the power m is 2, the error becomes a minimum. The standard deviation of the errors in the case of a flat plate with 316-nm out-of-plane displacement is 88 pm when n=1024 and m=2.

Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry

In this paper, a real-time shape measurement system using pixel-by-pixel calibration tables is developed. We proposed a shape measurement method using pixel-by-pixel calibration tables produced with multiple reference planes. In this method, all the relationships between the phase of the projected grating and the spatial coordinates can be obtained for each pixel. This method excludes a lens distortion and intensity errors of the projected grating in measurement results theoretically. Tabulation makes short-time measurement possible. The linearity of each pixel of a camera is also corrected using pixel-by-pixel calibration tables for linearity immediately after grabbing images.

Development of real-time shape measurement system using whole-space tabulation method

In this paper, we apply phase-shifting digital holographic interferometry to simultaneous measurement for out-of-plane and in-plane displacements by employing two beam illuminations for an object. Phase-shifted holograms before and after displacements of the object using each of two beams are recorded by a CCD camera, separately. The complex amplitude at each pixel of the CCD plane is analyzed from the holograms taken with phase-shifting. The complex amplitude of he object is reconstructed from the complex amplitude distribution on the CCD plane using the Fresnel diffraction integral. Each directional phase difference distribution is obtained by calculating the phases before and after deformation for each directional beam. The phase distribution for out-of-plane displacements is obtained by calculating the sum of the two phase difference distributions. The phase distribution for in-plane displacements is obtained by calculating the difference of the two phase difference distributions. The phase values provide accurate displacement distribution information. Actually, when the object deforms in both out-of-plane and in-plane directions, it is possible to analyze the displacement distribution in each direction. The theory and an experiment are shown.

Simultaneous Measurement of Out-of-Plane and In-Plane Displacements by Phase-Shifting Digital Holographic Interferometry

Digital holography is useful to reconstruct three-dimensional shapes of objects. The reconstruction process of the objects is fast and accurate because the reconstruction is performed by computer calculation without developing photographic plate. Phase-shifting digital holographic interferometry is possible to measure shape and displacement of objects quantitatively. The authors developed windowed phase-shifting digital holographic interferometry (WPSDHI) which provides very accurate results by decreasing the effect of speckle noise.

Toru Matui

Papers

Accurate pixel-to-pixel correspondence adjustment in a digital micromirror device camera by using the phase-shifting moiré method.

Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry

Development of real-time shape measurement system using whole-space tabulation method

Simultaneous Measurement of Out-of-Plane and In-Plane Displacements by Phase-Shifting Digital Holographic Interferometry

Three-Dimensional Displacement Analysis by Windowed Phase-Shifting Digital Holographic Interferometry