Lensless Three-Dimensional Quantitative Phase Imaging Using Phase Retrieval Algorithm

Abstract

Quantitative phase imaging (QPI) techniques are widely used for the label-free examining of transparent biological samples. QPI techniques can be broadly classified into interference-based and interferenceless methods. The interferometric methods which record the complex amplitude are usually bulky with many optical components and use coherent illumination. The interferenceless approaches which need only the intensity distribution and works using phase retrieval algorithms have gained attention as they require lesser resources, cost, space and can work with incoherent illumination. With rapid developments in computational optical techniques and deep learning, QPI has reached new levels of applications. In this tutorial, we discuss one of the basic optical configurations of a lensless QPI technique based on the phase-retrieval algorithm. Simulative studies on QPI of thin, thick, and greyscale phase objects with assistive pseudo-codes and computational codes in Octave is provided. Binary phase samples with positive and negative resist profiles were fabricated using lithography, and a single plane and two plane phase objects were constructed. Light diffracted from a point object is modulated by phase samples and the corresponding intensity patterns are recorded. The phase retrieval approach is applied for 2D and 3D phase reconstructions. Commented codes in Octave for image acquisition and automation using a web camera in an open source operating system are provided.

Keywords: computational optics; digital imaging; holography; lensless imaging; phase retrieval; quantitative phase imaging; three-dimensional imaging.

Figure 1

Optical configuration of lensless incoherent quantitative phase imaging (QPI) system and the schematic of the phase retrieval algorithm.

Figure 2

Amplitude simulated at (a) d₂ = 10 cm, (c) d₂ = 15 cm and (e) d₂ = 20 cm. Phase simulated at (b) d₂ = 10 cm, (d) d₂ = 15 cm and (f) d₂ = 20 cm. The phase retrieved after (g) 2, (h) 10 and (i) 50 iterations and the (j) original phase. (k) Plot of C (x = 0, y = 0) as a function of number of iterations.

Figure 3

Image of the test objects (a) Swinburne logo at the object plane and (b) Swinburne emblem at the sensor plane. Reconstructed amplitude at (c) the object plane and (d) the sensor plane. Retrieved phase at (e) the object plane and (f) the sensor plane.

Figure 4

(a) Amplitude and (b) phase of the optical field at the sensor plane. Phase reconstruction by the phase retrieval algorithm at (c) d₂ = 20 cm and (d) d₂ = 40 cm. (e) Plot of the correlation coefficient as a function of number of iterations.

Figure 5

(a) Scattering layers synthesized using Fourier Gerchberg–Saxton algorithm (GSA) with a scattering ratio σ = 0.12. (b) Amplitude and (c) phase of the field at the sensor plane and (d) reconstructed phase after 20 iterations. (e) modulo-2π representation of a linear phase with a maximum phase of 8π. (f) Amplitude and (g) phase of the field at the sensor plane and (h) reconstructed phase after 20 iterations. (i) Original phase at the sample plane. (j) Reconstructed, unwrapped phase at the sensor plane. (k) Comparison of modulo-2π phase profile of the original and reconstructed phase patterns.

Figure 6

Images of the two test objects (a) Swinburne logo and (b) Star object. Optical microscope images of (c) Swinburne logo and (d) Star object. Intensity pattern recorded by the image sensor for (e) Swinburne logo and (f) Star object. Phase map generated by the phase retrieval algorithm after two iterations for (g) Swinburne logo and (h) Star object. The phase images generated by the phase retrieval algorithm after two iterations for (i) Swinburne logo and (j) Star object.

Figure 7

(a) Optical microscope image of the fabricated object. (b) Thick object construction using two thin objects. Phase reconstruction results for (c) star object and (d) ‘Nan’ object. (e) 3D QPI reconstruction.