Development of spatial and temporal phase evaluation techniques in digital holography 6

CHAPTER SIX CONCLUSIONS AND FUTURE WORK 6.1 Conclusions The main objectives of this thesis are to develop new spatial and temporal phase evaluation techniques in digital holography, an

CHAPTER SIX CONCLUSIONS AND FUTURE WORK

6.1 Conclusions

The main objectives of this thesis are to develop new spatial and temporal phase evaluation techniques in digital holography, and to overcome the existing problems in some practical applications with the digital holographic technique The main conclusions drawn from the research work in this thesis are summarized as follows: (1) In the spatial domain, a new method based on the concept of complex phasor is proposed to determine the phase difference map (or wrapped phase map) and higher-order displacement derivatives in digital holography Hence, not only the deformation distribution of a test object is obtained, but higher-order displacement derivatives, such as first-order and second-order displacement derivatives, are also determined Sine/cosine transformation and short-time Fourier transform are further proposed to process the extracted wrapped phase maps It is demonstrated that high-quality phase distributions corresponding to higher-order displacement derivatives can

be obtained In addition, since the shifting operation is digitally performed, the accuracy is effectively ensured

(2) In the spatial domain, a fringe density estimation of wrapped phase maps is also studied in digital holography, and a new algorithm using an advanced analysis approach (i.e., short-time Fourier transform) is proposed to estimate the fringe density After the phase map is determined at each state, a phase difference map is directly obtained by a digital phase subtraction method Since the phase difference map

obtained is noisy, a filtering algorithm is applied to reduce the noise before phase unwrapping Subsequently, a phase unwrapping algorithm is required to correct the

π

2 jumps of the filtered wrapped phase map In many cases, a priori knowledge on

fringe density distributions is useful in the selection or development of filtering algorithms and phase unwrapping algorithms In this study, both simulation and experimental results demonstrate that the proposed method is feasible and effective, and can effectively and accurately estimate the fringe density of a noisy wrapped map Compared with previous techniques (such as continuous wavelet transform), the proposed method can more effectively suppress the influence of speckle noise It is also illustrated that the estimated fringe density distribution is close to the theoretical distribution

(3) In the temporal domain, an improved short-time Fourier transform is proposed to study the dynamic cases A series of reconstructed phase images is first obtained by using a reconstruction algorithm in digital holography The proposed method is then applied to process the series of reconstructed phase maps pixel by pixel With the proposed method, each sequence (i.e., each pixel along the time axis) can possess a window size Hence, this proposed method can also be considered as an adaptive method, and the improved short-time Fourier transform can effectively overcome the problems existing in the conventional continuous wavelet transform and short-time Fourier transform The proposed method is then applied to study the continuous deformation of a cantilever beam and profiling of an object with height steps The experimental results demonstrate that compared with the previously proposed methods (such as the conventional temporal phase unwrapping), the proposed method in this thesis is able to perform better especially in the suppression

of speckle noise

(4) In the temporal domain, detection and compensation of phase-shifting error

in phase-shifting digital holography are also investigated Three novel methods, such

as spectral analysis, are proposed to detect the phase-shifting error and enhance the quality of reconstructed images It is demonstrated that without a compensation operation, the resultant phase-contrast map is contaminated by a twin-image, and high-contrast results can not be obtained With the proposed detection and compensation methods, phase-shifting error generated during the calibration procedure can be effectively and accurately detected It is also illustrated that a preset detection step of the proposed algorithm plays an important role in the search of the phase-shifting error, and the proposed method can accurately detect the phase-shifting errors in phase-shifting digital holography The results demonstrate that the proposed methods are feasible and effective

(5) In the applications with digital holographic technique, the extension of the depth of focus for a particle field measurement is studied It is demonstrated that a disadvantage of conventional particle field measurements in digital holography is the small depth of focus In this case study, a focal plane is obtained for each pixel along

a series of reconstruction distances based on the proposed entropy method, and a depth map is then determined Finally, a synthesized extended focused image is obtained by using the extracted depth map, and all particles are in focus In addition, wavelet modulus maxima algorithm and Canny algorithm are further proposed to detect the edges of the particles, and the sizes and a 3D localization of the particles are also determined The results illustrate that the proposed method is feasible and effective in extending the depth of focus Since only one single digital hologram at each instant is required, the proposed technique could also find applications in the measurement of other physical parameters, such as particle velocity

(6) In the applications with digital holographic technique, complex-valued object reconstruction is also investigated A simple but effective iterative method is proposed to quantitatively recover a complex-valued object from Fresnel diffraction

intensity Several diffraction intensity distributions are recorded through position shift

of a phase mask, and a new phase retrieval algorithm is designed It is demonstrated that reconstructed images are of high quality, and the proposed phase retrieval algorithm works well even with a small position shift In addition, a fast convergence rate is achieved, and no support constraint is required in the mask plane Although a visible laser source is applied, the proposed technique can also be used with other light sources, such as x-ray

(7) In the applications with digital holographic technique, optical image encryption has also been studied In this study, two novel methods based on the interference principle are proposed for optical color image encryption, and one more method using a bit-plane separation is proposed in order to enhance the security for optical image encryption using phase-shifting digital holographic technique The results demonstrate that the proposed methods not only can effectively encrypt the images, but also possesses a high security However, this security level in the proposed optical cryptographic system does not increase the difficulties of the decryption for the authorized receiver

6.2 Future work

The research work in this thesis has contributed significantly to the fundamental knowledge of digital holography, and has also overcome some existing problems in the practical applications with digital holographic technique Moreover, this research

work may also open up new research areas in the practical applications with digital holographic technique In this thesis, the proposed techniques are described and validated with simulation and experimental results However, since it is impossible to fully cover all aspects, it is recommended that some future work can be done based on this thesis to develop new techniques or improve the adaptability of the proposed techniques Among the potential work, the following issues can be further addressed (1) An entropy method is proposed to extend the depth of focus in a particle field measurement using digital holographic technique It is demonstrated that a proper selection of block size is important to ensure the accuracy of an extended focused image However, the selection of a block size is manually determined in this study, thus an optimal and automatic selection strategy [such as receiver operating characteristic analysis (Fawcett, 2006)] may be further investigated for the extension

of depth of focus in a particle field measurement

(2) In practical applications, complex-valued object reconstruction and optical image encryption are investigated in this thesis However, in these two cases, a digital device called spatial light modulator is not available in the laboratory, so an adequate simulation has been carried out instead With the availability of this device, the concept proposed in this thesis can be further proven with experimental results

(3) Digital holographic technique is applied to different application fields, such

as optical image encryption However, digital holographic principles have not been fully explored, and the principles in digital holography can be further studied to overcome other existing problems in practical applications For instance, the basic principle of interference in digital holography can be used to extract random-phase masks for optical image encryption, but can also be further studied for the multiple-image encryption not just for a single multiple-image encryption In addition, other advanced

algorithms can also be explored to enhance the security level or increase the number

of security keys in optical image encryption, and watermarking technique using optical principles can also be investigated

(4) In the conventional phase-shifting digital holography, a monochromatic light source is usually applied, thus color information of the test object is lost However, color information of test specimens has many useful applications not just for esthetic reasons Since effective post-processing methods were proposed in the past several years, the phase-shifting color digital holographic technique (Yamaguchi

et al., 2002) can be further developed In addition, digital holographic tomography (Yu and Chen, 2007) is also an interesting topic, and can be applied to many practical studies, such as biology and medicine (Momose et al., 1996; Momose, 2003; Choi et al., 2007) Hence, digital holographic tomography can be considered as another important and interesting research topic, and may be further studied