.--- .-. 

NASA Technical Memorandum 10233 1 

Speckle Interferometry Using Fiber 

Optic Phase Stepping 

Carolyn A. Mercer and Glenn Beheim 

Lewis Research Center 

Cleveland, Ohio 

Prepared for the 

Symposium on Optical and Optoelectronic Applied Science and Engineering 

sponsored by the Society of Photo-Optical Instrumentation Engineers 

San Diego, California, August 6-11, 1989 

[NASA -TM-j 0 23 3 1 ) S PECK32 INTER FEROM ETBY 

USING FIBER OPTIC PBASE STEPPING (NASA. 

Lewis Research Center) 9 p CSCL 14B 

I89- 2 7999 

Unclas 

G3/35 0224992 
3 

d 

0 

U3 

I 

'A 

Speckle interferometry using fiber optic phase stepping 

Carolyn R. Mercer and Glenn Beheim 

National Aeronautics and Space Administration 

Lewis Research Center 

21000 Brookpark Road, Cleveland, Ohio 44135 

ABSTRACT 

A system employing closed-loop phase-stepping is used to measure the out-of-plane 

deformation of a diffusely reflecting object. Optical fibers are used to provide 

reference and object beam illumination for a standard two-beam speckle interferometer, providing set-up flexibility and ease of alignment. Piezoelectric fiberstretchers and a phase-measurement/servo system are used to provide highly accurate 

phase steps. Intensity data is captured with a charge-injection-device camera, and 

is converted into a phase map using a desktop computer. 

The closed-loop phase-stepping system provides 90" phase steps which are accurate to 

0.02', greatly improving this system relative to open-loop interferometers. The system is demonstrated on a speckle interferometer, measuring the rigid-body translation 

of a diffusely reflecting object with an accuracy of =lo", or roughly 215 nm. This 

accuracy is achieved without the use of a pneumatically mounted optics table. 

1. INTRODUCTION I 

Speckle interferometry is a technique which measures deformations of diffusely 

reflecting objects using low spatial resolution detect0rs.l It is difficult to accurately interpolate between the resultant interferometric fringes, so phase-stepping 

techniques have been applied to speckle interferometry to provide direct digital processing of the phase measurements.2 The accuracy of these measurements can be limited by phase stepping error^.^ The phase modulator, usually a mirror mounted on a 

piezoelectric transducer, must first be calibrated, a procedure frequently complicated by transducer nonlinearity and hysteresis, as well as sensitivity drift caused 

by temperature fluctuations and changes in the optical layout. Nonuniform mirror 

motion, which causes the magnitude of the phase steps to vary as a function of position, is another common error source. Open-loop phase stepping systems are also subject to errors caused by random phase variations produced by vibration, temperature 

fluctuations, and air currents. 

This paper describes a phase-stepping speckle interferometer based on a highly accurate closed-loop phase-stepping system which uses a synchronous phase detection technique4 and an all-fiber optical system5 as described in Ref. 6. 

technique compensates for both phase modulator errors and random phase shifts caused 

by environmental disturbances of the optical fibers. The single-mode optical fibers 

provide spatially uniform phase fronts and a flexible optical delivery system. The 

phase-stepping speckle interferometer is used to measure the out-of-plane deflection 

of an aluminum blade. The measurements indicate the direction as well as the magnitude of displacement, and are made without using a pneumatically mounted vibration 

isolation table, demonstrating the stability that can be achieved with this system. 

This phase control 

The experimental apparatus is described first, followed by the method of data acquisition. Finally, phase measurements showing the displacement of an object are presented as phase maps, histograms and plots. 
2. EXPERIMENTAL APPARATUS 

A schematic of the optical system is shown in Fig. 1. The entire system is mounted 

on a honeycomb optical table without pneumatic vibration dampening. The dashed line 

represents an enclosure built around the speckle interferometer to reduce the effects 

of air turbulence. 

The object under study (OBJ) is a metal blade covered with retroreflective tape to 

increase its reflectivity. The object is mounted on a piezoelectrically-driven 

double-headed arrow. 

imaged with unity magnification through a 120 mm lens (L2) onto a 120 by 120 pixel 

charge-injection-device camera (CID). An aperture (A) is stopped down to approximately f/60, creating image-plane speckles larger than the camera's 28 1~m detector 

elements. To maximize the reflected light that passes through the aperture, the 

object is placed so that its normal bisects a, the 40" angle that the object beam 

makes with the camera's optical axis. 

translation stage (PZT3) to provide object displacement along the axis shown by the t 

Light from a fiber (Fobj) illuminates the object, which is 

Light emitted from another fiber (Fref) serves as a reference wavefront and is 

diverted to the camera by a 50:50 beamsplitting cube (BS). A lens/pinhole combination (L3/PH) creates a spatially filtered spherical wave which, to the camera, 

appears to originate from aperture A. The distances between each output fiber face 

and the camera are equal to within the 2 cm coherence length of the argon ion laser. 

The fiber optic system shown in Fig. 1 serves as a light delivery system for the 

speckle-interferometer and also provides for hig'nly accurate phase stepping. Light 

from an argon ion laser operating at 514.5 run is coupled through a lens (L1) into 

one leg (Fin) of a variable-ratio fiber-optic coupler (FC). This light is split 

into the path length matched LO m long output fibers F,bj and Fref used in the 

speckle interferometer. These fibers are single-mode nonpolarization-preserving 

fibers. Each output fiber is wrapped tightly around a piezoelectric transducer 

(PZTL and PZT2) forming a fiber optic phase-controller on each arm of the interferometer. A portion of the light traveling through each output fiber is reflected at 

the fiber's end face, and travels back through the coupler. The reflected light 

from each fiber combines interferometrically within the fourth leg of the fiberoptic coupler (Fsig) and is detected by a photodiode (PD). Defining the one-way 

phase delay of the light traveling through fibers Fobj and Fref to be 8,bj 

and eref respectively, the current generated by PD can be described as: 

ipD = KPD Io[1 + m cos(2eref - 2eobj)l (1) 

where K~D is the sensitivity of the photodetector, Io is the mean detected intensity, and m is the fringe visibility. A 10 kHz sicusoidal voltage applied to PZT1 

modulates ipD for synchronous detection by the closed-loop phase-control system; 

the modulated current is described by: 

ipD = K~D Io{l + m cos[28 - 213 sin(wt)l} (2) 

where 8 = (eref - eobj), and 13 and w are the amplitude and frequency of the 

phase modulation, respectively. 

A block diagram of the phase-control system is shown in Fig. 2. An oscillator (OSC) 

generates the modulation signal which drives PZTL. A lock-in amplifier (LOCK-IN) 

2 
compares the amplified signal from PD to the oscillator's driving frequency and 

generates a voltage (El) which is described by:6 

where is the gain of the lock-in amplifier, Kmp 

is the sensitivity of the current-to-voltage converter preamp, and J1() is the first 

order Bessel function. An integrator (INTI and a high-voltage amplifier (AMP) integrate and amplify E1 for use as an error signal. This error signal drives PZT2, 

changing the optical path length of Fref until E1 is nulled. When E1 is 

nulled, 0 equals either 0" or 180", depending on initial conditions. Changing the 

loop polarity allows 0 

with a computer controlled switch (SW2). In order to select between the two allowable values of 8, the initial conditions can be set by temporarily deactivating the 

feedback loop with a switch (SW1) and applying an offset voltage to PZTL to coarsely 

step the phase to the desired value, and then reactivating the phase-control system 

within 20 msec to lock onto and maintain the correct phase setting. This computercontrolled offset voltage is applied with a digital-to-analog converter (D/A). In 

this way, the relative phase between the light at the output fiber faces can be set 

to any multiple of go", i.e., 0, = (n - 1) (90") where n = 1, 2, 3, or 4. The root 

mean square phase step error was determined to be 0.02" by measuring the standard 

deviation in E1 and using Eq. (3).6 

C = KLI Kmp KPD Io m J1(2p), KLI 

to be set to 90" or 270".6 This sign change is accomplished 

3. DATA ACQUISITION 

The out-of-plane displacement of the object was measured using the fiber optic phasestepping interferometer. A voltage applied to PZT3 moved the object along the 

optical axis as shown by the double-headed arrow in Fig. 1. The phase of the light 

reflected off the surface of the object relative to the reference wave was measured 

before and after the object was translated, and a phase map y(x,y) was calculated 

showing the out-of-plane component of the distance that the object moved. 

In order to measure the phase of the light reflected off of the object relative to 

the reference wave, four images were acquired by the CID camera with the relative 

phase 8 stepped by 90" between exposures. The intensity field detected by the CID 

camera can be described as: 

In(x,y> = Io(x,y){l + m(x,y)cos[y(x,y> + en11 (4) 

where Io(x,y) is the average intensity detected by pixel (x,y>, m(x,y> is the Corresponding visibility, and @(x,y> is the relative phase of the object and reference 

waves caused by optical path differences between the output fibers' end faces and the 

camera. Four intensity maps In(x,y) are recorded while the object was in a reference position, and then four more were recorded after the object had been moved. 

The intensity maps were stored on a desktop computer via an eight-bit A/D card. 

Phase stepping and object translation were computer controlled, while an operator 

acquired images after each phase step. In order to provide adequate operator 

response time, there was a 5 sec pause between each phase step. A 10 sec delay was 

included to move the object and allow it to settle, for a total acquisition time of 

60 sec. No attempt was made to minimize this time; 1/30 sec for each frame capture 

and perhaps a 1 sec pause for object translation could reduce this time to less than 

3 sec. 

3 
The relative phase Q(X,Y) is determined at each pixel by using the standard phasestepping relation:' 

The phase at a give point was calculated only if the signal modulation (2IOm) 

exceeded a threshold Cth where:8 

and the threshold constant Cth was chosen to minimize the deviation in the calculated phase cp while maximizing the number of valid pixels. 

4. RESULTS 

At each validated point, the initial phase was subtracted from the final phase to 

determine the phase difference AW representing the motion of the object caused by 

voltage applied to PZT3. Figure 3 shows the phase difference measured across the 

120 by 120 pixel array when 19.2 V was applied to PZT3. The threshold constant 

Cth was set to 1/20 of the saturation intensity. The shaded pixels show the structure of the recorded speckle pattern; the level of grey indicates the value of Acp. 

Black areas represent invalid pixels. Slightly fewer than one-half of the pixels 

were considered invalid, primarily because more than one speckle was present at 

those pixels. 

The phase shifts calculated at each pixel are shown in Fig. 4 as histograms for each 

of four voltages applied to PZT3. This data shows that the object moved away from 

the detector when a voltage was applied, 360" represents no motion and 0" indicates 

a displacement of The widths of these histograms show that the uncertainty in the measured phase across the surface of the 

blade is about 10" rms. The average phase steps across the detector array were computed from the histograms. These average phase steps were measured eight times at 

each of nine voltages applied to PZT3. This data plotted in Fig. 5 shows that the 

error in the repeated measurement of the displacements was 6.8" on the average, and 

was as large as 14". The data was fit to a straight line and had a correlation coefficient of 0.988, showing that PZT3 was only approximately linear over the region 

that it was traversed. One data point lies far off of the general curve. This was 

the only point which passed the modulation threshold and yielded an incorrect measurement, in fact, the histogram for this point was very narrow. The most likely 

explanation for this erroneous point is operator error, probably caused by acquiring 

an image at the wrong time. Four of the 72 phase measurements were corrected for a 

180" phase stepping error. This error can be caused by any disturbance which alters 

the phase 8 by more than 180" during the 20 msec that the phase control system is 

under open-loop control. 

X/[2 cos2(a/2)] away from the detector. 

When nonrigid-body translation is to be measured, the phase at a single pixel can be 

tracked. Figure 6 shows the phase measured as a function of applied voltage for 

three randomly selected pixels. Although only three pixels are shown, all of the 

valid pixels show the same trend. 

4 
5. CONCLUSION 

A fiber optic phase stepping interferometer was demonstrated by measuring the out-ofplane motion of a rigid body with 210" accuracy without using a pneumatically mounted 

optical table. This system's inherent advantages include the flexibility of a fiber 

optic based optical configuration and the accuracy of closed-loop phase control. 

6. REFEREXCES 

1. R. Jones and C. Wykes, Holographic and Speckle Interferometry, Chapter 3, 

Cambridge University Press, Cambridge (1983). 

2. D.W. Robinson and D.C. Williams, "Digital Phase Stepping Speckle Interferometry," 

Optics Commun. 57(1), 26-30 (1986). 

3. C. Ai and J.C. Wyant, "Effect of Piezoelectric Transducer Nonlinearity on Phase 

I 

Shift Interferometry," Appl. Opt. 26(6), 1112-1116 (1987). 

4. D.B. Neumann and H.W. Rose, '*Improvement of Recorded Holographic Fringes by 

Feedback Control," Appl. Opt. 6(6), 1097-1104 (1967). 

5. M. Corke, J.D.C. Jones, A.D. Kersey and D.A. Jackson, "All Single-Mode Fibre 

Optic Holographic System with Active Fringe Stabilisation," J. Phys. E. 18(3), 

185-186 (1985). I 

6. C.R. Mercer and G. Beheim, "Active Phase Compensation System for Fiber Optic 

Holography," NASA TM-LO1295 (1988). 

7. J.C. Wyant, "Use of an ac Heterodyne Lateral Shear Interferometer with Real-Time I 

~ Wavefront Correction Systems," Appl. Opt. 14(11), 2622-2625 (1975). I 

8. K. Creath, "Phase-Shifting Speckle Interferometry," International Conference on 

Speckle, SPIE Proc. 556, H.H.Arsenault, Ed., 337-346 SPIE, Bellingham, WAY 

(1985). I 

5 
r----------- 1 

f I ,:,: i, I W Fref I 

I 

I 

PzTl 

L1 0 2YF F In F sig 

Figure 1. - Optical system for phase-stepping speckle interferometry. 

Figure 3. - 120 x 120 pixel phase map, 

19.2 volts applied to PzT3. 

sw2 

PzTl 

aFC ) 

6.4 VOLTS 

07 

Figure 2. - Phasecontrol electmnlcs. 

Figure 4. 

19.2 VOLTS 32.0 VOLTS 44.8 VOLTS 7 

c H t 

0 450 0 450 0 450 

NUMBER OF MEASUREMENTS 

Phase histograms for four applied voltages. 

6 
4M r 

0- 

8 

0 

Q 

8 

Q 

4M r =I-- 8 

ot 8 0 

-60 

-6 

11111111111 

0 61210243036424854 

APPLIED VOLTAGE, V 

Figure 6. - Phase measurement at lhree pixels. 

7 
NASA National Aeronautics and Report Documentation Page 

7. Key Words (Suggested by Author(s)) 

Speckle; Interferometry; Fiber optics; Phase stepping; 

Closed loop 

Space Administration 

1. Report No. I 2. Government Accession No. 

18. Distribution Statement 

Unclassified - Unlimited 

Subject Category 35 

NASA TM-102331 I 

9. Security Classif. (of this report) 20. Security Classif. (of this page) 

Unclassified Unclassified 

4. Title and Subtitle 

Speckle Interferometry Using Fiber Optic Phase Stepping 

21. No of pages 22. Price' 

8 A02 

7. Author(s) 

Carolyn R. Mercer and Glenn Beheim 

~~ ~ 

9. Performing Organization Name and Address 

National Aeronautics and Space Administration 

Lewis Research Center 

Cleveland, Ohio 44135-3191 

2. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Washington, D.C. 20546-0001 

3. Recipient's Catalog No. 

5. Report Date 

6. Performing Organization Code 

8. Performing Organization Report No. 

E-5040 

10. Work Unit No 

582-01-1 1 

11. Contract or Grant No. 

13. Type of Report and Period Covered 

Technical Memorandum 

14. Sponsoring Agency Code 

5. Supplementary Notes 

Prepared for the Symposium on Optical and Optoelectronic Applied Science and Engineering sponsored by the 

Society of Photo-Optical Instrumentation Engineers, San Diego, California, August 6- 1 1, 1989. 

6. Abstract 

A system employing closed-loop phase-stepping is used to measure the out-of-plane deformation of a diffusely 

reflecting object. Optical fibers are used to provide reference and object beam illumination for a standard twobeam speckle interferometer, providing set-up flexibility and ease of alignment. Piezoelectric fiber-stretchers and 

a phase-measurement/servo system are used to provide highly accurate phase steps. Intensity data is captured with 

a charge-injection-device camera, and is converted into a phase map using a desktop computer. The closed-loop 

phase-stepping system provides 90" phase steps which are accurate to 0.02", greatly improving this system 

relative to open-loop interferometers. The system is demonstrated on a speckle interferometer, measuring the 

rigid-body translation of a diffusely reflecting object with an accuracy of f lo", or roughly 15 nanometers. This 

accuracy is achieved without the use of a pneumatically mounted optics table. 

For sale by the National Technical Information Service, Springfield, Virginia 221 61 NASA FORM 1626 OCT 86