Two-step Phase-shifting Interferometry Research Articles

Asymmetric cryptosystem and software design based on two-step phase-shifting interferometry and elliptic curve algorithm

We propose an asymmetric cryptosystem based on two-step phase-shifting interferometry (PSI) and elliptic curve (EC) public-key cryptographic algorithm, in which one image is encrypted to two interferograms by double random-phase encoding (DRPE) in Fresnel domain and two-step PSI, and the session keys such as geometrical parameters and pseudo-random seeds, are asymmetrically encoded and decoded with the aid of EC algorithm. The receiver, who possesses the corresponding private key generated by EC algorithm, can successfully decipher the transmitted data using the extracted session keys. The utilization of EC asymmetric cryptosystem solves the problem of key management and dispatch, which is inevitable in the conventional optical symmetric cryptosystems. Not only computer simulation, but also software design and development are carried out to verify the feasibility of the proposed cryptosystem.

Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter

Parallel two-step phase-shifting interferometry for microscopy is presented, and the recording condition for generalized two-step phase-shifting interferometry is discussed. A 45° tilted cube beamsplitter enables to replicate the orthogonally linear polarized object and reference waves into two parallel beams, respectively. As a consequence, two interferograms with quadrature phase shift are obtained along the two beams, and phase reconstructed with an improved algorithm. To reconstruct the phase distribution from the two-step phase-shifting interferograms, a certain recording condition should be satisfied. However, the recording condition has not ever been discussed before. In this paper, the recording condition for the two-step phase-shifting interferometry is derived and that is: the intensity of reference wave should be no less than two times object wave intensity.

Parallel two-step phase-shifting point-diffraction interferometry for microscopy based on a pair of cube beamsplitters

Parallel two-step phase-shifting point-diffraction interferometry for microscopy based on a pair of cube beamsplitters is proposed. The first 45°-tilted cube beamsplitter splits object wave into two parallel copies: one copy is filtered by a pinhole in its Fourier plane to behave as reference wave, while the other one remains unchanged as object wave. The second cube beamsplitter combines the object and reference waves, and then split them together into two beams. Along with the two beams, two parallel phase-shifting interferograms are obtained in aid of polarization elements. Based on the proposed configuration, slightly-off-axis interferometry for microscopy is performed, which suppresses dc term by subtracting the two phase-shifting holograms from each other. The setup is highly stable due to its common-path configuration, and has been demonstrated to be suitable for measuring moving objects or dynamic processes.

Analysis and correction of object wavefront reconstruction errorsin two-step phase-shifting interferometry

The method of calculating and correcting object wave reconstruction errors caused by phase shift errors in two-step phase-shifting interferometry is studied systematically. Based on the principle of random distribution and the amplitude-phase independence of diffractive object wave, the expression of objective wave reconstruction error is introduced and the formula for that in the two-step standard algorithm is deduced. The automatic error correction method is suggested by further analyzing the structures, the characters of those errors caused by phase shift errors, and the objective expression. By the proposed method, the reconstructive amplitude and phase errors can be corrected at the same time through simple operation on the objective complex amplitude reconstructed by the standard two-step method without the additional measurement or the acknowledge of phase shift. The computer simulations are carried out to verify the effectiveness of this method, and the results show that the method is robust and reduces the effect of phase shift error on object wave-front reconstruction by about 2 orders of magnitude. Optical experiments also indicate that this method is effective and efficient.

Parallel phase-shifting interferometry based on Michelson-like architecture

In this paper, we present a new scheme for parallel phase-shifting interferometry that employs a Michelson-like architecture and a simple polarization unit to generate two phase-shifting interferograms with phase shift of π/2 at a single camera exposure. The parallel phase-shifting unit is built with simple optical components, and the distance between the parallel interferograms can be adjusted conveniently. Phase reconstruction is performed by using an algorithm developed for two-step phase-shifting interferometry. The practicability of the proposed configuration and the reconstruction method is demonstrated by experiments.

Parallel on-axis holographic phase microscopy of biological cells and unicellular microorganism dynamics

We apply a wide-field quantitative phase microscopy technique based on parallel two-step phase-shifting on-axis interferometry to visualize live biological cells and microorganism dynamics. The parallel on-axis holographic approach is more efficient with camera spatial bandwidth consumption compared to previous off-axis approaches and thus can capture finer sample spatial details, given a limited spatial bandwidth of a specific digital camera. Additionally, due to the parallel acquisition mechanism, the approach is suitable for visualizing rapid dynamic processes, permitting an interferometric acquisition rate equal to the camera frame rate. The method is demonstrated experimentally through phase microscopy of neurons and unicellular microorganisms.

Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm

A hybrid cryptosystem is proposed, in which one image is encrypted to two interferograms with the aid of double random-phase encoding (DRPE) and two-step phase-shifting interferometry (2-PSI), then three pairs of public–private keys are utilized to encode and decode the session keys (geometrical parameters, the second random-phase mask) and interferograms. In the stage of decryption, the ciphered image can be decrypted by wavefront reconstruction, inverse Fresnel diffraction, and real amplitude normalization. This approach can successfully solve the problem of key management and dispatch, resulting in increased security strength. The feasibility of the proposed cryptosystem and its robustness against some types of attack are verified and analyzed by computer simulations.

Image encryption based on gyrator transform and two-step phase-shifting interferometry

A novel optical image encryption method is proposed, based on gyrator transform and phase-shifting interferometry. The input two-dimensional image to be encrypted is gyrator transformed two times, and two random phase masks are placed at the input plane and the output plane of the first gyrator transform. Two-step phase-shifting interferometry is used to record the digital holograms of the input image encrypted by use of double-random phase encoding technique in gyrator transform domain. The rotation angles of gyrator transform, the random phase mask in the gyrator plane and the arbitrary phase shift used for recording form the keys for decryption of the input image. Numerical simulations are presented to verify its validity and efficiency.

Full-phase image encryption by two-step phase-shifting interferometry

We have proposed a full-phase image encryption method based on double random-phase encoding in Fresnel domain and pixel random permutation (PRP) technique with the use of two-step phase-shifting interferometry (PSI) we reported recently, and verified the effectiveness of this method and its robustness against occlusion and noise attacks by a series of numerical simulations. Comparing with other similar methods, this approach can decrease the number of the interferograms to be delivered from at least three needed in ordinary PSI to only two, give much better performance of image reconstruction than amplitude-based encryption, and provide much higher security level. This method is usable for both the gray-level images and binary images, and usually the latter will lead to better results.

Securing information using digital optics

We present a new method to secure information based on digital optics in this paper. The input image to be encrypted is recorded as interferograms by use of two-step phase-shifting interferometry. Before transmitting through communication channels, the interferograms are encrypted as phase codes in fractional Fourier domain by using a computer generated random phase mask. The set of fractional orders and the computer generated random phase mask form the keys to the encrypted data. With the phase shifts generated in the recording process, the original image can be retrieved from the correct decrypted interferograms successfully. Computer simulations are presented to prove its validity.

Two-step phase-shifting interferometry and its application in image encryption

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.