Method for Phase Resolved Heterodyne Shearographic Measurements

Abstract

A phase-resolved heterodyne shearing interferometer has been developed for high-rate, whole field observations of transient surface motion. The sensor utilizes polarization multiplexing and multiple carrier frequencies to separate each segment of a shearing Mach-Zehnder interferometer. Post-processing routines have been developed to recombine the segments by extracting the scattered object phase from Doppler shifted intermediate carrier frequencies, providing quantitative relative phase changes and information to create variable shear, phase resolved shearographic fringe patterns without temporal or spatial phase shifting.

Claims

1. A digital signal process to compute on a computer a phase resolved gradient of displacement based on phase resolved heterodyne shearographic measurements, the digital signal process comprising the steps of: accessing temporal spatial irradiance data stored on a computer as a sequence of pixel-based image frames; isolating heterodyne signal from a complete measurement by high-pass filtering each pixel independently to output heterodyne information at local oscillator frequencies of first and second carrier frequencies; multiplying each pixel by sine and cosine of the first carrier frequency to calculate in-phase and quadrature phase time sequences for the first carrier frequency; low pass filtering the resulting in-phase and quadrature time sequences to remove unwanted components predominantly at twice the first carrier frequency and produce first filtered in-phase and quadrature time sequences; producing an estimate of Doppler phase at each pixel for the first carrier frequency by arctangent demodulation of the first filtered in-phase and quadrature time sequences using the first carrier frequency; multiplying each pixel by sine and cosine of the second carrier frequency to calculate in-phase and quadrature phase time sequences for the second carrier frequency; low pass filtering the resulting in-phase and quadrature time sequences to remove unwanted components predominantly at twice the second carrier frequency and produce second filtered in-phase and quadrature time sequences; producing an estimate of Doppler phase at each pixel for the second carrier frequency by arctangent demodulation of the second filtered in-phase and quadrature time sequences using the second carrier frequency; applying a spatial offset to the Doppler phase from the second carrier frequency to adjust a shearing distance and output a spatially shifted estimate of Doppler phase for the second carrier frequency; subtracting the first carrier frequency estimate of Doppler phase from the spatially shifted estimate of Doppler phase for the second carrier frequency to produce a series of frames containing a relative phase between two segments of shearing interferometer; generating a shearogram by subtracting a phase image in a reference frame from a phase image in a target frame; applying an iterative phase filter for visualization of a phase image and noise removal; and applying an unwrapping routine to the phase image to yield a representation of gradient of displacement.

2. The digital signal process as recited in claim 1, further comprising the steps of: calculating an axial velocity for the first carrier frequency to produce whole-field velocity images for the first carrier frequency; and calculating an axial velocity for the second carrier frequency to produce whole-field velocity images for the second carrier frequency.

3. The digital signal process as recited in claim 1, wherein said iterative phase filter is applied for visualization and noise removal as follows: calculating a sine of phase; applying a mean filter to the sine of phase; calculating a cosine of phase; applying a mean filter to the cosine of phase; and recalculating the phase using a four quadrant arctangent.

4. The digital signal process as recited in claim 3, wherein said iterative phase filter is iteratively repeated to remove phase residues.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Additional advantages and features will become apparent as the subject invention becomes better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein:

[0010] FIG. 1 shows a laboratory sensor schematic of an exemplary heterodyne shearographic vibrometer with a dynamic diffuse-scatterer for the target.

[0011] FIG. 2 shows an exemplary phase resolved heterodyne shearographic measurements block diagram as it relates to the sensor schematic in FIG. 1.

[0012] FIG. 3 shows an exemplary processing sequence performed by the signal processor in FIG. 2 to produce displacement gradients and axial velocity for display.

DETAILED DESCRIPTION

[0013] FIG. 1 shows a laboratory sensor schematic of an exemplary heterodyne shearographic vibrometer 100 with a dynamic diffuse-scatterer for the target. Such an exemplary heterodyne shearographic vibrometer comprises a laser source 101; beam splitter 102; 50 beam expander 103; mirror 104; dynamic diffuse scatterer 105; 1000 mm plano-convex lens 106; polarizing filter 107; beam splitter 108; half wave plate 109; mirror 110; mirror 111; polarizing beam splitter 112; 3.5 beam, minimization and focusing 113 beam splitter 114; Acousto optic modulator (AGM) 115, 25 kHz downshift; mirror 116; half wave plate 117; AOM 118, 15 kHz downshift; mirror 119; polarizing beam splitter 120; 20 beam expander 121; beam splitter 122; focal plane array 123 (512512 pixels at 60,000 frames/s); trans impedance amplifier 124; signal processor and data display 125.

[0014] An exemplary method of operating a heterodyne shearographic vibrometer is also variously represented in FIGS. 2 and 3. For example, FIG. 2 shows an exemplary heterodyne shearographic measurements block diagram as it relates to the sensor schematic in FIG. 1. The source is a linearly polarized laser 101. A splitter 102 divides the source into a probe and reference beams. In the probe beam path, a beam expander 103, e.g., one or more lens, expand and collimate the probe (or measurement) beam, and mirror 104 redirects the beam to a dynamic object 105; the object has a diffuse surface. The electric field scatters from the moving object 105 and now has a random spatial phase or amplitude. The purpose of the invention is to determine changes to the surface displacement by tracking changes in the random, scattered electric field. As the object deforms, a phase shift is imparted due to the optical path change near the object plane 105. Thus, the optical field at the object is modified by a phase, associated with the new position of the object as follows:

[00001]$\begin{array}{cc}{u}_o\left(,\right).fwdarw.u_o\left(,\right).Math.e^{\frac{j.Math..Math.2.Math..Math..Math..Math..Math..Math.P}{}},& \left(1\right)\end{array}$

where is the optical wavelength.

[0015] Some of the resulting scattered radiation is collected by a single lens 106. The beam propagates through a dichroic polarizing filter 107 where the vertically polarized radiation is absorbed. A splitter 108 divides the beams into a shearing interferometer. A half wave plate 109 rotates the polarization 90 degrees. A mirror 110 redirects the rotated beam to a polarizing beam splitter 112 which combines the rotated beam with an unrotated beam from the splitter 108, which was redirected by mirror 111. Lens 113 focuses the combined beams from the splitter 112. The combined beams propagate to a non-polarizing splitter 122.

[0016] Following initial propagation through the beam splitter 102, the reference beam propagates to a splitter 114 dividing the beam into two reference beams. Each beam propagates through an acousto-optic modulator (AOM), 115 and 118. AOM 115 downshifts the frequency by one carrier frequency, 1. A mirror 116 redirects the beam to a half wave plate 117 which rotates the polarization 90 degrees. The beam then propagates to a polarizing beam splitter 120. AOM 118 downshifts the frequency by another carrier frequency, 2. A mirror 119 redirects the beam to the polarizing beam splitter 120. The combined beams propagate to a lens 121 which expands the beam. The combined beams propagate to the non-polarizing splitter 122 where they combine with the probe beams from lens 113.

[0017] The combined beams from 122 propagate the focal plane array 123 which transduces the irradiance of the fields into an electrical charge proportional to the irradiance, described by

I(x, y, t)=|R.sub.1.sup.2|+|R.sub.2.sup.2|+|M.sub.1.sup.2(x, y, t)|+|M.sup.2(x, y, t)|+2|R.sub.1||M.sub.1(x, y, t)|cos[.sub.1t+.sub.1(x, y, t)]+2R.sub.2||M.sub.2(x, y, t)|cos[.sub.2t+.sub.2(x, y, t)], (2)

where R.sub.1,2 are the reference segment amplitudes, M.sub.1,2 are the probe segment amplitudes, .sub.1,2 are the carrier frequencies, and .sub.1,2 are the phase shifts due to target motion which contains the random object phase.

[0018] A trans-impedance amplifier circuit 124 converts charge from the focal plane array 123 into a digital representation of the irradiance on a computer 125.

[0019] The sequence of image frames captured on the computer 125 undergoes a process on the same computer to calculate the phase resolved gradient of displacement as well as axial velocity. The process is outlined in FIG. 3.

[0020] The process to produce displacement gradients and axial velocity is based on extracting time varying phase shifts from multiple carrier frequencies. First, the image data stored on the computer 125 is accessed 201. The heterodyne signal is isolated from the complete measurement by high-pass filtering 202 each pixel independently. This filter removes R.sub.1.sup.2, R.sub.2.sup.2, and M.sub.2.sup.2 from the camera's representation of the optical field, equation 2. The filter 202 outputs the heterodyne information at the local oscillator frequencies .sub.1, .sub.2. In-phase and quadrature 203, 206 are calculated for each carrier frequency by multiplying each pixel by the sine and cosine of the local oscillator frequency. The resulting in-phase I.sub.demod and quadrature Q.sub.demod time sequences are low pass filtered 204, 207 to remove unwanted components predominantly at twice the carrier frequency as follows:

Q.sub.1,2(t)=LP[HP[I(t)]sin(.sub.1,2t)](3)

I.sub.1,2(t)=LP[HP[I(t)]cos(.sub.1,2t)](4)

The in-phase and quadrature terms are then processed in block 205, 208 that contains mathematical equation 4 and produces an estimate of the Doppler phase at each pixel.

[00002]$\begin{array}{cc}{}_{1,2}\mathrm{unwrap}\left[{\tan }^{-1}\left(\frac{Q_{1,2}\left(t\right)}{I_{1,2}\left(t\right)}\right)\right].& \left(5\right)\end{array}$

The axial velocity can be estimated for each carrier 221, 222 using the Doppler phase,

[00003]$\begin{array}{cc}v=\frac{}{4.Math..Math.}.Math.\left(\frac{}{t}\right).& \left(6\right)\end{array}$

The output of 221 and 222 are whole-field velocity images.

[0021] To continue with the calculation of displacement gradients, the output of 208 is spatially shifted, 209. The outputs of 205 and 209 subtracted, 210. The output is a series of frames containing the relative phase between both segments of the shearing interferometer. Shearographic image generation requires two sets of images, a reference with one deformation condition and a test case with another deformation condition. With the heterodyne technique, multiple frames have been acquired allowing investigation of numerous conditions. To generate the shearogram, the phase image from the reference frame should be subtracted from the phase image from the test frame, 211. For visualization and noise removal, are iterative phase filter is applied, 212-218. The sine, 213 and cosine, 215 of the phase is calculated and then a mean filter, 214 and 216 is applied to 213 and 215. The phase is then recalculated using a four quadrant arctangent, 217. This process needs to be repeated N times to remove phase residues, 218. Following noise removal, are unwrapping routine should be applied to the phase image, 219. This yields a phase resolved representation of the gradient of displacement, 220.

[0022] It is obvious that many modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as described.