Electronic speckle pattern interferometry usingdigital image processing techniques

Suezou Nakadate, Toyohiko Yatagai, and Hiroyoshi Saito

The use of digital image processing techniques for electronic speckle pattern interferometry is discussed.A digital TV-image processing system with a large frame memory allows us to perform precise and flexibleoperations such as subtraction, summation, and level slicing. Digital image processing techniques make iteasy compared with analog techniques to generate high contrast fringes. Some experimental verificationsare presented in the cases of surface displacement and vibration amplitude measurements.

1. Introduction

Since Butters and Leendertz introduced TV detec-tion and filtering techniques into speckle interferome-try,1 measurement of normal and in-plane displacementand vibration amplitude has been performed by severalauthors using analog signal processing techniques andanalog memories, i.e., by using a video tape recorder 2 3

or a scan converter memory tube.4 5 To measure de-formation of an object, its speckle image stored in amemory before deformation is subtracted electronicallyfrom the image after deformation. High-pass filteringand full-wave rectification of its video signal producea fringe pattern displayed on a monitor. This method,called electronic speckle pattern interferometry (ESPI),is now well developed and has some attractive featurescompared with conventional holographic interferome-try, i.e., the use of a low resolution device, short exposuretime, no need for photographic processing. Recently,Cookson et al. showed that the use of a very short laserbeam pulse enabled use of speckle interferometry usedin an industrial environment without any mechanicalisolation. 3

However, the analog ESPI technique so far has rela-tively poor accuracy and flexibility in signal processing,and therefore it is not easy to generate clear fringepatterns.

In this paper, an application of digital image pro-cessing techniques to ESPI is described. A special

The authors are with Rikagaku Kenyusho, Institute of Physical &Chemical Research, 2-1 Hirosawa, Wako-shi, Saitama 351, Japan.

Received 15 August 1979.0003-6935/80/111879-05$00.50/0.© 1980 Optical Society of America.

digital facility for processing a TV image is developed,and its advantages in ESPI are discussed referring tothe experimental results.

II. System Description

A schematic diagram of double-exposure ESPI formeasuring normal displacement is shown in Fig. 1. Thedigital image processing system consists of a high speedADC, a digital frame memory, a memory update con-troller, a nonlinear signal processor, and a DAC. Thissystem employs an analog preprocessor for level slicing*of a video signal and a digital nonlinear processor in-stead of a high-pass filter and a full-wave rectifier, whichare used in conventional ESPI. The light from aHe-Ne laser is expanded by an objective lens and is splitinto object illumination and reference surface illumi-nation beams by a beam splitter. Diffusely scatteredlight from object and reference surfaces is collected byan imaging lens and focused onto a Chalnicon target ofthe TV camera.

To perform double-exposure ESPI, the speckle imageon the target is converted into an electric video signal,which is sent to the ADC directly or after being changedto a binary signal by the analog level slicer. The ADCsamples the video signal to yield a digital picture madeup of 512 X 512 sample points. Each sample point isquantized to 256 discrete gray levels. The digital pic-ture can be stored in the digital frame memory in 1/30sec. After deformation of the object, the digitized videosignal of the deformed object is subtracted from that ofthe object before deformation by the memory updatecontroller, and the resultant signal is stored in thememory. This signal after subtraction is subjected topoint-by-point nonlinear processing such as level slicingand subsequently converted to an analog signal and fedto the video input of a monitor. On the monitor, in-terference fringes representing displacement of the

1 June 1980 / Vol. 19, No. 11 / APPLIED OPTICS 1879

Fig. 1. Schematic diagram of arrangement for normal displacementmeasurement. Digital image processing system consists of high speedADC, digital frame memory, memory update controller, nonlinear

signal processor, and DAC.

Output

(a) 255

0 255Input

Output

(b) 255-__

0 255Input

Output

(c) 255-

0 255Input 25

Fig. 2. Schematic representation of nonlinear processing for outputsignal: (a) half-wave rectification; (b) level slicing; and (c) one level

windowing.

object are displayed. In this case, the zero-order fringeis dark due to the subtraction process.

The image processing system shown in Fig. 1 hasmany functions: (1) summation and averaging of inputimages; (2) subtraction of an input image from anotherimage stored in the digital frame memory; (3) levelslicing of an image by which the gray levels less than acertain threshold level are mapped into the zero leveland the levels greater than or equal to the thresholdlevel into the 255th level; (4) level windowing of animage by which the gray levels within the two thresholdlevels are mapped into the 255th level and otherwiseinto the zero level; and (5) y correction of a digitizedimage stored in the memory.

These functions of the digital image processing sys-tem make it easy to generate high contrast fringes cor-responding to displacement and vibration modes ofobjects.

Ill. Experiments

A. Normal Displacement Measurement

The experimental setup for normal displacementmeasurement is already shown in Fig. 1. A chalnicontarget TV camera, model C1000 (Hamamatsu Corp.),was used. Since the resolution of the TV camera was700 TV lines at the central part of the chalnicon targetand the target was 10 X 10 mm, its spatial resolution was28.6ym. A 50-mW He-Ne laser (wavelength, 6328 A)and a Micro-NIKKOR lens (focal length, 105 mm) wereused. The object was a vertical metal strip 70 mm highand 67 mm wide covered with white powder of magne-sium oxide. This metal strip was clamped at its lowerend and loaded so that the deflection of the free upperend was along the line of sight, close to the TVcamera.

1. Fringes Obtained By PostprocessingAn electric video signal from the TV camera was di-

rectly sampled and quantized. The signal resultingfrom subtraction of two digital speckle patterns wassubjected to nonlinear postprocessing such as half-waverectification, level slicing, and level windowing whoseschematic representations are shown in Figs. 2(a)-(c).Figures 3(a)-(c) obtained by such operations show thatdigital nonlinear postprocessing generates high contrastfringes. The fringe patterns shown in Figs. 3(b) and (c)were obtained by level slicing at the 37th level and onelevel windowing at the 43rd level, respectively. Grayscale bars are also displayed at the lower part of themonitor as shown in Figs. 3(b) and (c).

In these experiments, the speckle size calculated fromXF was 6.3 um, where X is the wavelength, and F is thef/No. of the imaging lens. It should be noted that themeasurement has been performed even if the averagespeckle size is smaller than the spatial resolution of theTV camera. The reason is that a nonlinear operationsuch as level slicing enhances speckle contrast so as togive high contrast fringes. On the other hand, theconventional ESPI has to resolve fully speckle patternsto give high contrast fringes, because high-pass filteringis commonly employed instead of nonlinear operations.The same nonlinear operations as shown in Figs. 2(b)and (c) are performed by an analog limiter with suffi-cient gain, which has poor flexibility compared with thedigital implementation.

2. Fringes Obtained By PreprocessingFringes can be obtained by a binary image correlator

whose implementation is shown in Fig. 4. A video sig-nal from the TV camera is converted to a binary signalusing an analog level slicer. The binary speckle patternobtained after deformation of the object is subtractedfrom that before deformation. The resultant patternis subjected to nonlinear operation to give a fringe

1880 APPLIED OPTICS / Vol. 19, No. 11 / 1 June 1980

L

pattern. The experimental result obtained by such abinary correlator is shown in Fig. 5 for the case when thespeckle size is 19.0 um. The fringe pattern was dis-played by means of one level windowing at the 195thlevel.

Pre-processin -Di gjti- ProcessingI~ ~ ~ ~ __ 1 I- - - - -

I : I

> LevelSlice ;

… - . L _ _ _ .

Fig. 4. Implementation of a binary correlator using analog prepro-cessor of level slicing and digital operations.

Fig. 3. Fringes obtained by (a) half-wave rectification, (b) levelslicing at 37th level, and (c) one level windowing at 43rd level.

Fig. 5. Interferogram obtained by the binary correlator shown in Fig.4. Fringe pattern was displayed by means of one level windowing at

195th level.

When the analog level slicer of preprocessing is used,only one bit per pixel is enough to store the binaryspeckle pattern. Then it is possible to reduce data ofthe speckle pattern and the number of IC memories inthe digital image processing system.

B. Transient Behavior Measurement

The digital frame memory shown in Fig. 1 has a veryhigh input rate, i.e., 1/30 sec for each frame. Takingadvantage of this fact, transient behavior of a vibratingobject has been investigated with this ESPI. The objectwas an aluminum disk 80 mm in diameter and 0.1 mmthick fixed to a frame and excited at the central part ofthe object by a solenoid. The frequency of vibration ofthe object was 0.03 Hz. Compared with the input rateof the digital frame memory (1/30 sec), the period of thevibration (33 sec) was so large that fringe patterns de-picting normal displacement of the object could be ob-

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tained. The fringe patterns obtained are shown in Figs.6(a)-(c). The subtraction of two speckle patterns wasperformed at intervals of 0.5, 1.0, and 1.5 sec. Thesignal after subtraction was subjected to level slicing atthe 25th level.

(a)

EN~~~~~~~~~~l

(b)

(_

Fig. 6. Interferogram showing transient behavior of circular plateobtained by level slicing at 25th level. Object vibrated at 0.05 Hz, andsubtraction was carried out at intervals of (a) 0.5, (b) 1.0, and (c)

1.5 sec.

C. Lateral Displacement Measurement

The schematic diagram for the lateral displacementmeasuremert of a circular disk is shown in Fig. 7. Theobject to be measured was a glass disk 128 mm in di-ameter and 5 mm thick. The surface of the glass diskwas covered with white powder of magnesium oxide.The disk was illuminated by two symmetrical beamsand rotated about the center axis normal to its plane bya small amount to give lateral displacement. Thespeckle image of the object after rotation was subtractedfrom that before rotation and followed by level slicingto give an interferogram. Figure 8 shows a typicalfringe pattern when the speckle size was 8.6 um, and theobserved area was 20 X 20 mm at the central part of theobject. This fringe pattern was obtained by level slicingat the 10th level.

This experiment shows that lateral displacementmeasurement can be performed as in the case of normaldisplacement measurement, although the speckle sizeis smaller than the spatial resolution of the TV camera.Besides, it has been confirmed that the measurementcan be carried out by using the summation function ofthe digital image processing system even when the laser

Fig. 7. Schematic diagram of arrangement for lateral displacementmeasurement.

Fig. 8. Typical fringe pattern obtained for circular disk rotatingabout center axis normal to its plane. Signal after subtraction wassubjected to level slicing at 10th level. Average speckle size was 8.6

jim.

1882 APPLIED OPTICS / Vol. 19, No. 11 / 1 June 1980

Fig. 9. Typical vibration mode of object obtained by summation of 60 framesof speckle patterns. Signal after summation was subjected to level slicing at95th level. Frequency of vibration was 2.45 kHz. Brightest and secondbrightest fringes show vibration amplitudes of zero and 0.19 ,um, respectively.

power is weak. This fact shows that the SNR of the TVcamera can be improved by summation of images.Hence a high power laser is not necessary to perform themeasurement.

D. Vibration Analysis

With the interferometer shown in Fig. 1, vibrationamplitude measurements can also be carried out bymeans of the time-average method. The vibratingobject mentioned in Sec. II.B was used. The f/No. ofthe imaging system was chosen to be f/50. Speckleimages of each frame were summed 60 times by usinga summation function of the digital image processingsystem. This signal after summation was subjected tolevel slicing to give an interferogram. Figure 9 showsa typical fringe pattern when the object vibrated at 2.45kHz, and the observed area was 20 X 20 mm at thecentral part of the object. This fringe pattern was ob-tained by level slicing at the 95th level. In time-averagespeckle interferometry the reconstructed intensitydistribution of the fringe varies as J2[(47r/X)u(x,y)],where Jo is the zero-order Bessel function of the firstkind, X is the wavelength of the laser light, and u(x,y)is the vibration amplitude distribution across theobject.6 The brightest fringes in Fig. 9 correspond toa contour vibration amplitude of zero, and the secondbrightest fringes correspond to a vibration amplitudeof 0.19 im, where the fringe function J2 reaches thesecond maximum.

IV. Conclusion

Some applications of digital image processing tech-niques to ESPI have been described, and it has beenshown experimentally that the digital image processingsystem developed is well suited for measurement ofout-of-plane and in-plane displacement and vibrationamplitude of an object. Because speckle patterns aredigitized, arithmetical operations such as subtractionand summation between digitized speckle patterns, andnonlinear postprocessing such as level slicing are allperformed precisely and flexibly. Therefore, thesedigital techniques allow us to obtain easily high contrastfringes and ease restriction on the speckle size and thelaser power. A fringe pattern can be obtained whenspeckle patterns are converted to binary speckle pat-terns by using the level slicer of preprocessing. Thismeans that an inexpensive system, for example, a binarycorrelator, can be used.

Digital image processing techniques can be used inother speckle instrumentations such as contour, surfacestrain, and 3-D displacement measurements. Furtherdevelopment of techniques for such measurements arereported in another paper.

References1. J. N. Butters and J. A. Leendertz, Opt. Laser Technol. 3, 26

(1971).2. A. Macovski, S. D. Ramsey, and L. F. Schaefer, Appl. Opt. 10, 2722

(1971).3. T. J. Cookson, J. N. Butters, and H. C. Pollard, Opt. Laser Technol.

10, 119 (1978).4. 0. J. Lokberg, 0. M. Holje, and H. M. Pedersen, Opt. Laser

Technol. 8, 17 (1976).5. T. Nakajima and H. Saito, Jpn. J. Opt. 8, 91 (1979) (in Japa-

nese).6. L. Ek and N.-E. Molin, Opt. Commun. 2,419 (1971).

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