Abstract
Spectral-domain optical coherence phase microscopy (SD-OCPM) measures minute phase changes in transparent biological specimens using a common path interferometer and a spectrometer based optical coherence tomography system. The Fourier transform of the acquired interference spectrum in spectral-domain optical coherence tomography (SD-OCT) is complex and the phase is affected by contributions from inherent random noise. To reduce this phase noise, knowledge of the probability density function (PDF) of data becomes essential. In the present work, the intensity and phase PDFs of the complex interference signal are theoretically derived and the optical path length (OPL) PDF is experimentally validated. The full knowledge of the PDFs is exploited for optimal estimation (Maximum Likelihood estimation) of the intensity, phase, and signal-to-noise ratio (SNR) in SD-OCPM. Maximum likelihood (ML) estimates of the intensity, SNR, and OPL images are presented for two different scan modes using Bovine Pulmonary Artery Endothelial (BPAE) cells. To investigate the phase accuracy of SD-OCPM, we experimentally calculate and compare the cumulative distribution functions (CDFs) of the OPL standard deviation and the square root of the Cramér-Rao lower bound (1/ square root 2SNR ) over 100 BPAE images for two different scan modes. The correction to the OPL measurement by applying ML estimation to SD-OCPM for BPAE cells is demonstrated.
Highlights
The development of phase imaging modalities may permit quantitative measurements on the structure and dynamics of cellular specimens [1,2,3]
Several phase imaging methods have been investigated including: 1) noninterferometric methods [4], 2) digital holographic microscopy [5], 3) full-field phase microscopy based on a programmable spatial light modulator [6], 4) Fourier fringe analysis [7], 5) and Hilbert transform [8]
We formulate a theory for the probability distribution function (PDF) for the phase and intensity in spectral-domain optical coherence phase microscopy (SD-OCPM) [10] and demonstrate a good agreement between the theoretical and experimental probability density function (PDF)
Summary
The development of phase imaging modalities may permit quantitative measurements on the structure and dynamics of cellular specimens [1,2,3]. The recent application of SD-OCT to phase measurement has resulted in significant improvements in phase stability, sensitivity, and speed compared with those of time-domain OCT based systems [12]. We present ML estimated Bovine Pulmonary Artery Endothelial (BPAE) cell intensity, SNR, and OPL images for two different scan modes. To investigate phase precision of our SD-OCPM using two different scan modes, the cumulative distribution functions (CDFs) of OPL standard deviation and the square root of the CRLB over 100 images are calculated and compared. We validate our proposed ML estimator by acquiring 100 quantitative phase contrast images of a BPAE cell using SDOCPM for two scan modes and show the improved measured phase by the ML estimator
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