Researching | Lock-in incoherent differential phase contrast imaging

Journals >Photonics Research >Volume 10 >Issue 1 >Page 237 > Article

Photonics Research
Vol. 10, Issue 1, 237 (2022)

Lock-in incoherent differential phase contrast imaging

Chiara Bonati^*, Damien Loterie, Timothé Laforest, and Christophe Moser

Author Affiliations

Laboratory of Applied Photonics Devices, School of Engineering, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

show less

DOI: 10.1364/PRJ.445896 Cite this Article Set citation alerts

Chiara Bonati, Damien Loterie, Timothé Laforest, Christophe Moser. Lock-in incoherent differential phase contrast imaging[J]. Photonics Research, 2022, 10(1): 237 Copy Citation Text

show less

Abstract

We introduce a lock-in method to increase the phase contrast in incoherent differential phase contrast (DPC) imaging. This method improves the phase sensitivity by the analog removal of the background. The use of a smart pixel detector with in-pixel signal demodulation, paired with synchronized switching illumination, provides the basis of a bit-efficient approach to emulate a lock-in DPC. The experiments show an increased sensitivity by a factor of up to 8, as expected from theory, and a reduction of collected data by a factor of 70, for equivalent standard DPC measurements; single-shot sensitivity of 0.7 mrad at a frame rate of 1400 frames per second is demonstrated. This new approach may open the way for the use of incoherent phase microscopy in biological applications where extreme phase sensitivity and millisecond response time are required.

\tilde{I} ({\vec{u}}_{c}) = B δ ({\vec{u}}_{c}) + H_{abs} ({\vec{u}}_{c}) \tilde{μ} ({\vec{u}}_{c}) + H_{ph} ({\vec{u}}_{c}) \tilde{φ} ({\vec{u}}_{c}),

(1)

View in Article

B = \iint S ({\vec{u}}^{'}) {| P ({\vec{u}}^{'}) |}^{2} d^{2} {\vec{u}}^{'},

(2)

View in Article

H_{ph} ({\vec{u}}_{c}) \propto i [\iint S ({\vec{u}}^{'}) P^{*} ({\vec{u}}^{'}) P (- {\vec{u}}_{c} + {\vec{u}}^{'}) d^{2} {\vec{u}}^{'} - \iint S ({\vec{u}}^{'}) P ({\vec{u}}^{'}) P^{*} ({\vec{u}}_{c} + {\vec{u}}^{'}) d^{2} {\vec{u}}^{'}] .

(3)

View in Article

S (\vec{u}, t) = {\begin{matrix} S (\vec{u}) & for 0 + k T \leq t < \frac{T}{2} + k T \\ S (- \vec{u}) & for \frac{T}{2} + k T \leq t < T + k T \end{matrix} .

(4)

View in Article

\tilde{I} ({\vec{u}}_{c}, t) = B δ ({\vec{u}}_{c}) + H_{ph} ({\vec{u}}_{c}, t) \tilde{φ} ({\vec{u}}_{c}) = {\begin{matrix} B δ ({\vec{u}}_{c}) + H_{ph} ({\vec{u}}_{c}) \tilde{φ} ({\vec{u}}_{c}) & for 0 + k T \leq t < \frac{T}{2} + k T \\ B δ ({\vec{u}}_{c}) - H_{ph} ({\vec{u}}_{c}) \tilde{φ} ({\vec{u}}_{c}) & for \frac{T}{2} + k T \leq t < T + k T \end{matrix} .

(5)

View in Article

A = \sqrt{I^{2} + Q^{2}}, φ = \arctan 2 (I, Q) - \frac{π}{4} .

(6)

View in Article

CNR \propto \frac{F^{- 1} {2 H_{ph} ({\vec{u}}_{c}) \tilde{φ} ({\vec{u}}_{c})}}{\sqrt{B}},

(7)

View in Article

S (\vec{u}) = K \cdot S_{norm} (\vec{u}),

(8)

View in Article

K = \iint S (\vec{u}) d^{2} \vec{u}, \iint S_{norm} (\vec{u}) d^{2} \vec{u} = 1 .

(9)

View in Article

H_{ph} (\vec{u}) = B \cdot H_{norm} (\vec{u}),

(10)

View in Article

CNR \propto \sqrt{B} \cdot F^{- 1} {2 H_{norm} ({\vec{u}}_{c}) \tilde{φ} ({\vec{u}}_{c})} .

(11)

View in Article

\frac{{CNR}_{lock-in}}{{CNR}_{standard}} = \frac{1}{\sqrt{r}} .

(12)

View in Article

T_{IQ} = \frac{T_{lock-in} \cdot k}{2} .

(13)

View in Article

CNR \propto \sqrt{T \cdot n},

(14)

View in Article

\frac{{CNR}_{lock-in}}{{CNR}_{standard}} = \sqrt{\frac{T_{IQ}}{T_{LR}}} .

(15)

View in Article

B_{lock-in} = \frac{B_{standard} \cdot T_{IQ}}{T_{LR}} .

(16)

View in Article

{CNR}_{S, m a x} \propto \sqrt{W} \cdot F^{- 1} {2 H_{norm} ({\vec{u}}_{c}) \tilde{φ} ({\vec{u}}_{c})} .

(B1)

View in Article

k_{\max} r B_{S} = W \Rightarrow k_{\max} = \frac{W}{r B_{S}}, {CNR}_{L, m a x} \propto \sqrt{k_{\max} B_{S}} \cdot F^{- 1} {2 H_{norm} ({\vec{u}}_{c}) \tilde{φ} ({\vec{u}}_{c})} = \sqrt{\frac{W}{r}} \cdot F^{- 1} {2 H_{norm} ({\vec{u}}_{c}) \tilde{φ} ({\vec{u}}_{c})} .

(B2)

View in Article

\frac{{CNR}_{L, \max}}{{CNR}_{S, \max}} = \sqrt{\frac{1}{r}} .

(B3)

View in Article

Figures&Tables (9)

References (32)

Copy Citation Text

Chiara Bonati, Damien Loterie, Timothé Laforest, Christophe Moser. Lock-in incoherent differential phase contrast imaging[J]. Photonics Research, 2022, 10(1): 237

Download Citation

Set citation alerts for the article

Set citation alerts for the article

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address