Beating temporal phase sensitivity limit in off-axis interferometry based quantitative phase microscopy

Abstract

Phase sensitivity determines the lowest optical path length (OPL) value that can be detected from the noise floor in a quantitative phase microscopy (QPM) system. The temporal phase sensitivity is known to be limited by both photon shot-noise and a variety of noise sources from electronic devices and environment. To beat temporal phase sensitivity limit, we explore different ways to reduce different noise factors in off-axis interferometry-based QPM using laser-illumination. Using a high electron-well-capacity camera, we measured the temporal phase sensitivity values using non-common-path and common-path interferometry based QPM systems under different environmental conditions. A frame summing method and a spatiotemporal filtering method are further used to reduce the noise contributions, thus enabling us to push the overall temporal phase sensitivity to less than 2 picometers.

Transmission-Matrix Quantitative Phase Profilometry for Accurate and Fast Thickness Mapping of 2D Materials

“…In DPM, the temporal phase sensitivity δϕ t is limited by the intrinsic photon shot-noise, other than the environmental fluctuations . δϕ t follows the 1 / normalΔ N relation, where Δ N is the effective full-well-capacity (EFWC) . To further scale down the phase sensitivity, a specially designed high full-well-capacity (HFWC) camera (Q-2A750m/CXP-6, Adimec; full-well-capacity of 2 million electrons) is implemented, as illustrated in Figure e.…”

“…In this section, we will first characterize both the temporal and spatial phase sensitivities of our DPM system to ensure a high phase sensitivity is realized in experiments, and then we will scale down the phase sensitivity to the limit. Under the shot-noise limit, the temporal phase sensitivity of our TM-QPP system follows the relation δ ϕ normalt ≈ 1 m · normalΔ N , where Δ N is the EFWC that can be estimated from the histogram of the interferogram as illustrated in Figure e, while m is the effective number of pixels in the diffraction spot that is calculated to be around 11 based on our system configuration. To characterize the phase sensitivity of our system, we measured time-series of interferograms at a fixed frame rate of 500 frames per second (fps) with an exposure time of 1936 μs and calculated the temporal phase sensitivity in the form of OPD as OP normalD normalt = λ 0 · δ ϕ normalt 2 π .…”

“…To characterize the influence of the unevenness on geometric thickness mapping, we calculated the standard derivation of the background region (the whole area except for the sample region) in Figure f which was found to be around 0.11 nm. The signal-to-noise ratio in Figure f can be also calculated as 32.3 dB, by using the method proposed in previous work . Therefore, although the system phase sensitivity is high enough to resolve monolayer materials, the ultimate measurement limit may lie in the flatness of the substrate.…”

“…, 39 where ΔN is the EFWC that can be estimated from the histogram of the interferogram as illustrated in Figure 1e, while m is the effective number of pixels in the diffraction spot that is calculated to be around 11 based on our system configuration. To characterize the phase sensitivity of our system, we measured time-series of interferograms at a fixed frame rate of 500 frames per second (fps) with an exposure time of 1936 μs and calculated the temporal phase sensitivity in the form of OPD as…”

“…The signal-to-noise ratio in Figure 4f can be also calculated as 32.3 dB, by using the method proposed in previous work. 39 Therefore, although the system phase sensitivity is high enough to resolve monolayer materials, the ultimate measurement limit may lie in the flatness of the substrate. This becomes more obvious when imaging thinner monolayer structures, e.g., graphene.…”