The correction of the piezoelectric device

controller. For the purpose of correc

ig.

There are two control modes in our digital PZT

ting the deviation between the command of position control and voltage control in z direction, we measured the axial response curve several times by the command of position control and voltage control respectively (as shown in Fig.8 (a) and (b)). Then, we chose the same dynamic range (0.4μm) from these linear area to compare their variation of intensity. These data were averaged and shown in Fig.8(c). In this figure, we can see that the averaged variable range of intensity by position control is larger than voltage control. According to this result, we calculated the correction factor between position command and voltage command was,

On the other hand, for the purpose of correcting the deviation between the command of position control and voltage control in x and y directions, we scan a test target whose interval between linear pair is 10μm (the total length is 1mm). Fig.9 and F 10 show the test target image observed from optical microscope (4X, 50X, and 100X objectives).

l and voltage

Fig.9. oscope (4X objective).

Fig.8. The axial response curve for the command of position contro

control. (a) The axial response curve for the command of position control. (b) The axial response curve for the command of voltage control. (c) The variation of intensity for same dynamic range (0.4μm) between position control and voltage control.

The test target image observed from optical micr

Fig.10. The test target image from optical microscope(50X, 100X objective).

Then, we scanned this test target by the DCM. The scanning pixel was 64 x 64, scanning area was 64μm x 64μm. The image is shown in fig.11 (a).

Fig.11. The image of test target obtained from the DCM. (a) DCM image. (b) we selected three parts of intervals from Fig.11(a) and averaged these data.

Although we set the scanning area to 64μm x 64μm, the image was actually only 50μm x 50μm ( the interval between linear pair is 10μm ) in the Fig.11(a). So, we selected three parts of intervals and averaged these data (i.e. in Fig.11(b)). On this basis, we calculated the correct factor as

.

.2 Axial resolution

axial response curve of a mirror in our DCM setup. The full width

Fig.12. Measured axial response curve of a mirror.

In order to obtain surface profile from axial response curve, we estimate the axial r

e (r) could be obtained by dividing the variable signal (ΔI) by the

3

Fig. 12 shows the

at half maximum (FWHM) of main peak is about 0.8μm by using a NA 0.8 objective that is deviated from the theoretical value, 0.697μm, may caused by the aberration effect [14, 15](as showed in the inset of Fig.12).

esolution from the slope of the linear dynamic range. Depend on this slope, the surface variation of sample will cause the change of signal. In the linear area, the variation of light intensity(ΔI) and the height of sample (Δh) have the relational formula：Δh = ΔI / r.

Therefore, the slop

distance of movement (Δh). According to the slope, we can know the variable

information of sample height. The axial resolution is defined by the uncertainty (ΔE), which is the noise mainly from the fluctuation of the light source, mechanical vibration of the optical system and so on. In perfect situation, the variation of the signal is a straight line during the linear area. Even if the fluctuation of noise comes into existence, we also can use a straight line to fit the measured signal. Consequently, the depth resolution is defined as the uncertainty of the sample height, is equal to Δ E/r. Then, the axial resolution is better if the value of ΔE/r is lower.

In order to estimate the value of ΔE/r, the signal during the linear area was norma

The axial resolution is represen En․D. The ΔEn is the value of avera

lized. The maximum value is 1, and the minimum value is 0. The relation between the slope r and the dynamic range D is,

ted as Δ

ge noise which after intensity normalization. In Fig.13, the measured data points were fitted by a straight line of slope r after the signal normalization. In addition, the uncertainty ΔE is 0.841% and the dynamic range is 0.5μm. So, the axial resolution in our setup is about 4.2nm, and the dynamic range is 500nm for an objective with NA=0.8.

Fig.13. Linear signal of our differential confocal microscope with objective 100x NA=0.8, the uncertainty ΔE = 0.841%, dynamic range=500nm, so the depth resolution =4.2nm.

3.3 Lateral resolution

To demonstrate the lateral resolution in our developed DCM system, we scan the edge of a cover glass fin X direction and Y direction individually. After the intensity is normalized that we can obtain the data shown in Fig. 14(a) and 14(b).

According to the method [16], the transverse resolution is decided from the distance between the intensity is 0.2 and 0.8. We observed that the lateral resolution is different from X and Y direction. The resolution in X direction is about 0.677μm while that in Y direction is only 0.422μm.

Fig.14. Scanning the edge of a cover glass to measure the lateral resolution. (a) the resolution in X-axis is about 0.677μm, (b) the resolution in Y-axis is about 0.422μm.

Based on this finding, we try to alter the scanning program to change the scanning velocity of PZT, i.e. it will stay longer time for each pixel in X direction.

Thus, we increased the stay time for 0.01, 0.02, 0.03, 0.05 second for each pixel in X direction. In Fig.15, the sample is a test target (Edmund, T39-857), and the image of the edge of the pattern was improved distinctly from blurred to clear.

Fig.15. By altering the scanning program, the image was improved from blurred to clear. (a) Stay 0.01 second for each pixel in X direction (b) Stay 0.02 second for each pixel in X direction. (c) Stay 0.03 second for each pixel in X direction. (d) Stay 0.05 second for each pixel in X direction.

3.4 Signal-to-noise ratio

We measured the signal-to-noise ratio (SNR) fin our setup by a dynamic signal analyzer (Stanford Research System, SR780). The spectrum of the confocal reflectional signal is shown in Fig.16, and the mainly noise was seen at 60 Hz. Hence, the SNR is about 75.7dB.

Fig.16. The spectrum of the confocal reflectional signal obtained from a dynamic signal analyzer.

Chapter 4 Results

4.1 Microlens

First, We measured the surface profile of microlens and compared with the images observed from a common optical microscope in Fig.17(a) and a scanning electron microscope in Fig.17(b). As a matter of fact, the diameter of these mirolens is 1μm.

Fig.17. The image of microlens. (a) The image observed in optical microscope. (b) The image acquired from the scanning electron microscope(SEM).

Fig.18 shows our DCM image where pixel number is 256 x 256 and scanning area is 25.6μm x 25.6μm. The height of microlens is represented in the top and right inset of Fig. 18. The measured result of microlens is about 150nm height and 1μm diameter that is identical with the SEM measurement.

Fig.18. The DCM image of microlens.

4.2 Polymer Membrane

The surface image of a polymer membrane obtained from a optical microscope is shown in Fig.19.

Fig.19. The surface image of a polymer membrane from the optical microscope.

Fig.20 shows the results of our DCM measurement. The roughness of a polymer membrane can be seen apparently. Because this polymer membrane is a kind of material to compose the artificial vascular graft, investigate the roughness of membrane surface is important. If the situation for capability of coagulation and anti-coagulation between this material and blood is unbalanced, it will bring about thrombus.

Fig.20. The DCM image of a polymer membrane.

4.3 1-D Phase Grating

we diagnosed the surface features of holographic optical elements and compared with those images from atomic force microscope (AFM). Fig.21(a) shows an AFM image of a phase grating with 5μm x 5μm image size. Fig.21(b) shows the 1-D profile along the line of Fig.21(a), the average height of the grating is about 475nm, and the average period is about 1.03μm.

The surface image obtained by our DCM system is shown in Fig.21(c), the pixels is 128 x 128 and scanning area is 5.12μm x 5.12μm. Fig.21(d) shows the 1-D profile along the line of Fig.21(c), the average height of the grating is about 500nm, and the average period is about 1.1μm.

Fig.21. The AFM and DCM image of the 1-D phase grating. (a) AFM image of the grating. (b) 1-D profile along the line of Fig.21(a). (c) DCM image of the grating. (d) 1-D profile along the line of Fig.21(c).

Fig.22(a) shows an AFM image of a phase grating with 5μm x 5μm image size. Fig.22(b) shows the 1-D profile along the line of Fig.22(a), the average height of the grating is about 140 nm, and the average period is about 1.05μm. Then, the

obtained DCM image is shown in Fig.22(c) where pixel number is 128 x 75 and scanning area is 7.17μm x 4.2μm. The 1D profile along the line of Fig.22(c) is shown in Fig.22(d), the average height in this grating is about 150nm and the average period of the grating is about 1.1μm. Although the grating fabricated was not uniform, and the scanning area was different from AFM and DCM, the results can be comparable.

Fig.22. The AFM and DCM image of 1-D phase grating. (a) AFM image of the grating. (b) 1-D profile along the line of Fig.22(a). (c) DCM image of the grating.

(d) 1-D profile along the line of Fig.22(c).

4.4 2-D Photonic crystal

Finally, we measured the surface features of holographic optical elements, 2-D photonic crystal, and compared with those images from scanning electron microscope (SEM) and atomic force microscope (AFM).

Fig.23 shows a SEM image of a 2-D photonic crystal with 8.7μm x 12.8μm image size. It can be seen that the period of the 2-D photonic crystal is about 1.1μm.

Fig.23. The SEM image of a 2-D photonic crystal. The scale bar is 5μm.

On the other hand, Fig.24(a) shows an AFM image of the 2-D photonic crystal with 5μm x 5μm image size. It displays not only the surface profile of the grating, but also the information about depth. Fig.24(b) shows the 1-D profile along the line of Fig.24(a). we can see the maximum and minimum depth are labeled about 301.82nm and 25.32nm individually, the measured depth is approximately 276.5nm.

Fig.24. The AFM image of 2-D photonic crystal. (a) shows an AFM image of the 2-D photonic crystal with 5μm x 5μm image size. (b) shows the 1-D profile along the line of Fig.23(a).

Then, the obtained DCM image is shown in Fig.25(a) where pixel number is 128 x 128 and scanning area is 10.2μm x 10.2μm. Fig.25(b) shows the 1-D profile along the line of Fig.25(a). In Fig.25(b), the average depth about 300nm is measured and the average period is around 1.05μm. Although the 2-D photonic crystal fabricated was not uniform, and the scanning area was different in SEM, AFM and DCM, the results can be comparable.

Fig.25. The DCM image of the 2-D photonic crystal. (a) DCM image. (b) shows the 1-D profile along the line of Fig.25(a).

4.5 lateral resolution improvement

Finally, we used the Maximum likelihood estimation (MLE) algorithm to improve our DCM image performance.

These deblurred image are shown as below,

1. Microlens

Fig.26. The MLE image of microlens. (a) The measured lateral PSF in our setup.

(b) The DCM image of microlens. (c) After MLE algorithm, the image of microlens was deblurred and more sharpness.

2. Polymer Membrane

Fig.27. The MLE image of polymer membrane. (a) The measured lateral PSF in our setup. (b) The DCM image of polymer membrane. (c) After MLE algorithm, the image of polymer membrane was deblurred and more sharpness.

3. 1-D Grating

Fig.28. The MLE image of 1-D grating. (a) The measured lateral PSF in our setup. (b) The DCM image of grating. (c) After MLE algorithm, the image of grating was deblurred and more sharpness.

4. 2-D Photonic crystal

Fig.29. The MLE image of 2-D photonic crystal. (a) The measured lateral PSF in our setup. (b) The DCM image of 2D photonic crystal. (c) After MLE algorithm, the image of the grating was deblurred and more sharpness.

From the above results, lateral PSF was obtained by scanning the edge of cover glass, the images which iterated after MLE algorithm are more distinct than raw images.

Chapter 5 Discussion and conclusion

In this thesis, we have developed a DCM system and improve its resolution by using MLE algorithm. Using the nanometer depth sensitivity of DCM, we have measured the surface profile of several devices, including microlens, polymer membrane, one-dimensional phase grating and two-dimensional photonic crystal successfully. The advantages of DCM technique includes,

(1) When the height variation in a sample is extreme small, the edge effect will be strengthened on the axial height by the DCM technique.

(2) Grating and photonic crystal will not be broken after the measurement by DCM.

(4) User can change objectives with different NA according to the property of the sample, to correspond with all kinds of dynamic range and resolution we needed.

Moreover, if combing transmission detection configuration in out existing refection mode DCM setup. The technique can obtain not only the surface profile of the microlens, but also the focal length and spot size. These information will be helpful for microlens fabrication which can applied in photonics, optoelectronics, biology, medicine, and material science [20, 21, 22].

However, because the MLE algorithm based on the system measured may not describes the transfer characteristics of the imaging system under all conditions [23,

24], an accurate PSF should be measured under conditions that exactly replicate the conditions under which the image was acquired. This approach is impractical as each sample has its own optical characteristics that are not easy to replicate provided that they can be measured to a reasonable accuracy.

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