Experiment

A first experiment was performed to confirm that the spectrum of the light reflected from the object could be measured by using the proposed system. The experiment was carried out with the set-up shown in Fig. 3-1. A plane mirror was used as the target object. The actual spectrum of the light reflected from the target object is shown in Fig. 3-2, in which the full width at half maximum (FWHM) ranged from 487 nm to 740 nm. A PZT (PZ 94E, Physik Instrumente) was used to modulate the optical wavefront. The PZT was moved at velocities of 10 µm/s, 20 µm/s, and 30 µm/s. The modulation of the optical intensity of the interference fringes caused by the motion of the PZT was simulated by (3-8) and is shown in Fig. 3-4(a), 5(a) and 6(a) for the three PZT velocities.

The simulation results were then compared with the experimental ones. In the experiment, the object and reference wave were superimposed on a CMOS image sensor (Redlake; MotionScope M5) with a pixel size of 13.68 µm. The distance from the CMOS sensor to the object mirror was 300 mm. Considering the maximum temporal frequency of the optical intensity of the interference pattern when the reference mirror was moved with a velocity of 30 µm/s, the frame rate of the camera was set at 500 fps. The 500 hologram frames recorded by the camera for 1 s were used to investigate the variation of the optical intensity in time, and the experimental results are shown in Fig. 3-4(b), Fig. 3-5(b) and Fig.

3-6(b). The actual temporal spectra of the optical intensity were calculated by DFFT, and the results are shown in Fig. 3-7(a), (b), (c). In this case, the frequency step calculated by Eq. (3-17) was 1 Hz. The FWHM spectrum of the optical intensity corresponding to PZT velocities of 10, 20, and 30 µm/s were 27–41 Hz, 54–82 Hz, and 81–123 Hz, respectively.

Based on Eqs. (3-11) and (3-12), the FWHM spatial frequencies of the light source were estimated from 487 nm to 740 nm, from 487 nm to 741 nm, and from 487 nm to 740 nm.

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It can be seen that the spectrum of the light reflected from the object measured in the experiment was approximately the same as that measured with a spectrometer. In this case the, the object is plane mirror so the spectrum of the light reflected from the object and the spectrum of the light source are same. This means the experiment can be used to measure the spectrum of the light source as well.

Fig. 3-3. Actual spectrum of the light source measured with a spectrometer.

Fig. 3-4. (a) Time-varying intensity profile of one pixel simulated using actual spectrum of the light source and PZT velocity of 10 µm/s, and (b) experimental profile obtained from the center pixel of the recorded holograms for comparison.

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Fig. 3-5. (a) Time-varying intensity profile of one pixel simulated using actual spectrum of the light source and PZT velocity of 20 µm/s, and (b) experimental profile obtained from the center pixel of the recorded holograms for comparison.

Fig. 3-6. (a) Time-varying intensity profile of one pixel simulated using actual spectrum of the light source and PZT velocity of 30 µm/s, and (b) experimental profile obtained from the center pixel of the recorded holograms for comparison.

Fig. 3-7. The intensity spectrum of the hologram obtained from the Fourier transform of the center pixel of the recorded holograms with PZT velocities of (a) 10 µm/s, (b) 20 µm/s, and (c) 30 µm/s.

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The second experiment was conducted to examine the effect of errors caused by environmental disturbances or experimental devices (e.g., PZT calibration) on the reconstructed 3D information of the object with different wavelengths. In this experiment SW- and TW-LCDH were applied. The velocity of the PZT was set to 20 µm/s, and the maximum frequency and sampling frequency were estimated using Eqs. (3-11) and (3-14), respectively. The frame rate of the CMOS camera was 1000 fps (fs = 1000 Hz). The camera was set to record for 1s (N = 1000). The frequency step calculated using Eq. (3-15) was 1 Hz.

Fig. 3-8. The effect of errors caused by environmental disturbances or experimental devices on the reconstructed 3D information of the object with different selected wavelengths.

Each selected frequency in the optical intensity spectrum specified the wavelength via Eq. (3-13) and the complex amplitude via Eq. (3-15). The specific complex amplitude allowed us to use SW-LCDH to reconstruct a 3D image of the object, which was then compared with the original one with a root mean square (RMS) method to evaluate the accuracy. In this case, because the original object was considered to be a perfect flat plane,

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its center line was simply considered as a horizontal line which can be obtained from the cross-section along the center line of the reconstructed object. The RMS error calculated from the cross-section along the center line of the reconstructed object and the original object for each selected frequency was divided by the corresponding wavelength, and the results in Fig. 8 show that for the wavelength which was selected out of spectrum of the light source, the RMS errors are very larger.

To measure a steep object, we employed TW-LCDH, in which two different frequencies were selected in the optical intensity spectrum, and the corresponding wavelengths and complex amplitudes were calculated by using Eq. (3-11) and Eq. (3-13), respectively. The equivalent wavelength was calculated by Eq. (3-14). In this experiment, for simplicity, fb1 was set to a constant value of 82 Hz, and fb2 was varied. The results are shown in Table 3-1.

Table 3-1. The effect of errors caused by environmental disturbances or experimental devices on the reconstructed 3D information of the object with different selected equivalent wavelengths.

fb1 (Hz) 82 82 82 82 82 82

fb2 (Hz) 55 60 65 70 75 80

λ1 (×10^-3 µm) 488 488 488 488 488 488 λ2 (×10^-3 µm) 727 667 615 571 533 500 λe (µm) 1.481 1.818 2.353 3.333 5.714 20.000 RMS Error (×10^-2 µm) 0.457 0.489 0.555 0.649 1.410 3.728

RMS Error/λe (×10^-3) 3.1 2.7 2.2 1.9 2.5 1.8

The third experiment was conducted to examine the dependence of the quality of the reconstructed 3D image on the velocity of the PZT, which is directly proportional to the maximum equivalent wavelength according to Eq. (3-18) when employing TW-LCDH.

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The experiment was carried out with the CMOS camera at a frame rate of 1000 fps. The optical intensity spectrum was obtained from 1000 frames. The results of employing TW-LCDH are shown in Table 3-2. The velocity of the PZT was set at 10 µm/s, 20 µm/s, and 30 µm/s. The experiment results showed that, as the speed of the PZT was set higher, a larger error occurred. This can be explained by the increasing vibrations with increasing PZT velocity.

Table 3-2. The dependence of the quality of the reconstructed 3D image of the object on the velocity of the PZT when employing two-wavelength DH.

vR (µm/s) 10 20 30

fb1 (Hz) 33 66 99

fb2 (Hz) 32 65 98

λemax (µm) 20 40 60

RMS Error (×10^-2 µm) 1.19 2.82 4.18 RMS Error /λemax (×10^-3) 0.6 0.7 0.7

The fourth experiment was conducted to verify the effectiveness of the proposed method to measure 3D information of an actual object. A plane mirror tilted by a small angle was used as the target object. The velocity of the PZT was set to 20 µm/s, and the frame rate of the Pro Motion Camera was set to 500 fps (Δt = 1 ms), as in the first experiment. The intensity spectrum of the hologram was also from 54 Hz to 82 Hz.

The TW-LCDH method was applied. Two different frequencies, fb1 = 66 Hz and fb2

= 64 Hz, were selected in the temporal spectrum of the optical intensity. Two corresponding wavelengths, λ1 = 606 nm and λ2 = 625 nm, were estimated by using Eq. (3-13), and the equivalent wavelength, λe = 20 µm, was estimated by using Eq. (3-18). The surface of the object reconstructed by TW-LCDH, a cross-section, and error profile are

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shown in Fig. 3-9(a), (b) and (c), respectively. The value of RMS error calculated from the error profile was 0.024 µm, which was about 833 times smaller than the equivalent wavelength. Again the frequency of 53 Hz was selected in the intensity spectrum, and SW-LCDH was applied to reconstruct a 3D image of the object with less error, as shown in Fig. 3-10. In this case, the profile of the object obtained by TW-LCDH was used to detect and compensate for the 2π ambiguity error of the phase. The value of RMS error calculated from the error profile was 0.009 µm, which was about 84 times smaller than the wavelength.

Fig. 3-9. (a) Surface of an object reconstructed by TW-LCDH, (b) cross-section, and (c) error profile along center line.

Fig. 3-10. (a) Surface of the object reconstructed by SW-LCDH, (b) cross-section, and (c) error profile along center line.

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It is has been proven that each selected frequency in the optical intensity spectrum specified the complex amplitude via Eq. (3-15). The phase and amplitude information of the complex amplitude corresponding to the selected frequency allow reconstructing the intensity image and 3D image of the object. In the fifth experiment, the tilted mirror was replaced by a chromatic object that was a printed photo of 3 characters R, G and B on the dark background as shown in Fig. 3-11. The reference mirror was moved with a velocity of 20 µm/s, the frame rate of the camera was set at 500 fps. The 500 hologram frames recorded by the camera for 1 s. The variations of the optical intensity in time obtained from different color pixels and their spectrum are shown in Fig. 3-12(a), (b), (c) and (d), respectively. The FWHM spectrum of the optical intensity corresponding to red, green, blue and background pixels were 56–68 Hz, 72–82 Hz, and 76–86 Hz, and 57-82 Hz showed in Fig. 3-13.

Fig. 3-11. The chromatic object

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Fig. 3-12. Time-varying intensity profile of one pixel obtained from (a) the red, (b) green, (c) blue and (d) back-ground pixels of the recorded holograms.

Fig. 3-13. The intensity spectrum of the hologram obtained from the Fourier transform of the red, green, blue and back-ground pixels of the recorded holograms.

For each selected frequency in the optical intensity spectrum, the complex amplitude is specified by Eq. (3-15). The intensity images corresponding to selected frequencies were shown in Fig. 3-14. From the experiment results in Fig. 3-13 and Fig.

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3-14, it can be seen that the proposed method is possible to be used to reveal the spectral property of the target object.

Two different frequencies, fb1 = 62 Hz and fb2 = 63 Hz corresponding to two wavelength λ1 = 645 nm and λ2 = 635 nm in the red light region, were selected. The equivalent wavelength, λe = 40 µm, was estimated by using Eq. (3-18). The surface of the object reconstructed by TW-LCDH was shown in Fig. 3-15(a). The cross-sections along the areas marked by red, green and blue lines on the surface of the object were respectively shown in Fig. Fig. 3-15 (b), (c) and (d).

The surface of the object was also scanned by a confocal microscopy, the cross-section measured by the confocal microscopy at the same positions that were marked by red, green and blue lines in Fig. 3-15(a) were used to evaluate the accuracy of the measurement. The value of RMS error calculated from the error profile along red, green and blue lines were 0.327 µm, 0.724 and 0.963, which were 122, 55 and 41 times smaller than the equivalent wavelength, respectively. Because the selected wavelengths were in the red light region, the intensity of pixels corresponding to the green or blue points on the surface of the object were very weak as shown in Fig. 3-14. For the green or blue points on the surface of the object, these selected wavelengths were out of spectrum, this explained why RMS errors along green and blue lines were much more larger than the RMS error along red one.

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Fig. 3-14. The intensity image corresponding to selected frequency.

Fig. 3-15. (a) Surface of the object reconstructed by SW-LCDH, cross-section along (b) red, (c) green and (d) blue color character.

Another experiment was also performed as shown in Fig. 3-16, the reference mirror is moved by PZ 94E-Physik Instrumente Piezoelectric with velocity of 16µm/s, the practical spectrum of the light source measured by spectrometer is from 400 nm to 889 nm.

Similarly, CMOS camera (Redlake; MotionPro Y4 Lite) pixel Size with pixel size of 13.68µm was used, the holograms were recorded with 500fps, and two objective lens with

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the same characteristics were used to magnify the object. The object in this case was a layer of onion skin.

CCD

Halogen light source

Aperture

Object OL

OL Mirror

BS

PZT

Fig. 3-16. Experimental setup

Fig. 3-17. The spectrum of the light source was measured by spectrometer.

Fig. 3-18. A holographic image of the object recorded by fast CCD camera

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e

Fig. 3-19. The spectrum of the reflected light measured by proposed method corresponding to two point A and B indicated on the Fig. 3-18.

Fig. 3-20. The intensity image corresponding to selected frequency and wavelength of the light source

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Fig. 3-21. Phase profiles of the object were measured with two selected frequencies of (a) 69Hz, (b) 68Hz then (c) the profile of the object was reconstructed with two corresponding wavelengths.

The spectrum of the light source was shown in Fig. 3-17, an holographic image of the object recorded by fast CCD camera was shown in Fig. 3-18. The spectrum of the light reflected from two points on the object surface were measured by proposed method and the result was shown in Fig. 3-19. The intensity image corresponding to selected frequency and wavelength of the light source and the object profile calculated by two selected wavelengths were shown in Fig. 3-20 and Fig. 3-21, respectively.