Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy

Pinhas Girshovitz; Natan T. Shaked

doi:10.1364/OE.21.005701

Optics Express
Vol. 21,
Issue 5,
pp. 5701-5714
(2013)
•https://doi.org/10.1364/OE.21.005701

Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy

Pinhas Girshovitz and Natan T. Shaked

Open Access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Pinhas Girshovitz and Natan T. Shaked, "Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy," Opt. Express 21, 5701-5714 (2013)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Related Topics
Table of Contents Category
- Microscopy
Optics & Photonics Topics
?

The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: November 1, 2012
- Revised Manuscript: December 24, 2012
- Manuscript Accepted: January 1, 2013
- Published: March 1, 2013
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 8, Iss. 4

Abstract

We present a simple-to-align, highly-portable interferometer, which is able to capture wide-field, off-axis interference patterns from transparent samples under low-coherence illumination. This small-dimensions and low-cost device can be connected to the output of a transmission microscope illuminated by a low-coherence source and measure sub-nanometric optical thickness changes in a label-free manner. In contrast to our previously published design, the $τ$ interferometer, the new design is able to fully operate in an off-axis holographic geometry, where the interference fringes have high spatial frequency, and the interference area is limited only by the coherence length of the source, and thus it enables to easily obtain high-quality quantitative images of static and dynamic samples. We present several applications for the new design including nondestructive optical testing of transparent microscopic elements with nanometric thickness and live-cell imaging.

Full Article | PDF Article

More Like This

Off-axis digital holographic camera for quantitative phase microscopy

Zahra Monemhaghdoust, Frédéric Montfort, Yves Emery, Christian Depeursinge, and Christophe Moser
Biomed. Opt. Express 5(6) 1721-1730 (2014)

LED based large field of view off-axis quantitative phase contrast microscopy by hologram multiplexing

Mugdha Joglekar, Vismay Trivedi, Vani Chhaniwal, Daniel Claus, Bahram Javidi, and Arun Anand
Opt. Express 30(16) 29234-29245 (2022)

Off-axis setup taking full advantage of incoherent illumination in coherence-controlled holographic microscope

Tomáš Slabý, Pavel Kolman, Zbyněk Dostál, Martin Antoš, Martin Lošťák, and Radim Chmelík
Opt. Express 21(12) 14747-14762 (2013)

Previous Article Next Article

Supplementary Material (1)

Media 1: MPEG (148 KB)

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.

Fig. 1 Schematic system diagrams of: (a) the conventional τ interferometer [20]; (b) the off-axis τ interferometer. L1,L2 – lenses in a 4f configuration, BS – beam splitter, M1,M2 – mirrors, P – pinhole, RR – retro-reflector made of a two-mirror construction.

Download Full Size | PDF

Fig. 2 Explanation for the retro-reflector (RR) operation using ray tracing of the sample and the reference beams in the off-axis τ interferometer, as it would be seen if they were on the same optical axis.

Download Full Size | PDF

Fig. 3 The off-axis τ interferometer, connected in the output of an inverted microscope, which is illuminated by a tunable low-coherence source. MO – microscope objective, L0,L1,L2 – lenses, where L1 and L2 are in a 4f configuration, BS – beam splitter, M,M2 – mirrors, P – pinhole, RR – two-mirror retro-reflector. Inset: Wide-field off-axis interferogram of red blood cells obtained with the system, and its cross-section at the location indicated by the white line.

Download Full Size | PDF

Fig. 4 OPD sensitivities in a dry sample: (a) Spatial sensitivity: OPD standard deviation across a single OPD map for each of the 150 OPD maps. (b) Temporal sensitivity: OPD standard deviation for each diffraction-limited spot across the 150 OPD maps.

Download Full Size | PDF

Fig. 5 OPD maps of a volume phase holographic grating obtained under low-coherence illumination by: (a) the off-axis τ interferometer; and (b) the off-axis Mach-Zehnder interferometer.

Download Full Size | PDF

Fig. 6 SEM image of an element similar to our first lithographed phase target.

Download Full Size | PDF

Fig. 7 OPD maps of the first phase target created by FIB lithography, containing variable depths elements (see Fig. 6), as obtained using: (a) the off-axis τ interferometer with a low-coherence source; (b) the off-axis Mach-Zehnder interferometer with a low-coherence source; and (c) the off-axis Mach-Zehnder interferometer with a high-coherence source (HeNe laser).

Download Full Size | PDF

Fig. 8 OPD maps of the second phase target created by FIB lithography, containing variable depth elements, as obtained using: (a) the off-axis τ interferometer with a low-coherence source; (b) the off-axis Mach-Zehnder interferometer with a low-coherence source; and (c) the off-axis Mach-Zehnder interferometer with a high-coherence source (HeNe laser).

Download Full Size | PDF

Fig. 9 OPD and physical thickness maps of RBCs, obtained using a low-coherence source in: (a) the off-axis τ interferometer; and (b) the off-axis Mach-Zehnder interferometer. The standard deviation of the OPD and of the physical thickness maps for: (c) the off-axis τ interferometer; and (d) the off-axis Mach-Zehnder interferometer.

Download Full Size | PDF

Fig. 10 Measurements of Blepharisma organism swimming in water using the off-axis τ interferometer, demonstrating the system capabilities for quantitative imaging of fast dynamics on relatively large field of view due to its true off-axis configuration, and as opposed to the conventional τ interferometer [20]. See video in Media 1.

Download Full Size | PDF

Fig. 11 Schematics of the sample and immersion medium thicknesses and refractive indices.

Download Full Size | PDF

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

θ = arc \tan (Δ y / f),

I = 〈 | V_{s} + V_{r} |^{2} 〉 = I_{s} + I_{r} + G_{+ 1} + G_{- 1} .

G_{+ 1} = \sqrt{I_{s} I_{r}} \times \exp [- \frac{| O P D_{t o t a l} |}{l_{c} (x, y)}] \times \exp [- j \frac{2 π}{λ} O P D_{t o t a l}] \times \exp [- j \frac{2 π}{λ} y \sin (θ)],

O P D_{s} (x, y) = [{\bar{n}}_{s} (x, y) - n_{m}] \times h_{s} (x, y),

{\bar{n}}_{s} (x, y) = \frac{1}{h_{s} (x, y)} \int_{0}^{h_{s} (x, y)} n_{s} (x, y, z) d z .

G_{+ 1} = 〈 V_{s}^{*} (t) \times V_{r} (t + τ) 〉 = \sqrt{I_{s} I_{r}} \times \exp [- \frac{| τ |}{τ_{c}}] \times \exp [- j 2 π \frac{c}{λ} τ],

\begin{matrix} t_{1} = \frac{d}{c}; t_{2} = \frac{1}{c} {[d - h_{m} (x, y)] + [h_{m} (x, y) - h_{s} (x, y)] \times n_{m} (x, y) + h_{s} (x, y) \times {\bar{n}}_{s} (x, y)}; \\ τ = t_{2} - t_{1} = \frac{1}{c} {h_{s} (x, y) \times [{\bar{n}}_{s} (x, y) - n_{m} (x, y)] + h_{m} (x, y) \times [n_{m} (x, y) - 1]}, \end{matrix}

\begin{array}{l} O P D_{t o t a l} (x, y) = c \cdot τ \\ = h_{s} (x, y) \times [{\bar{n}}_{s} (x, y) - n_{m} (x, y)] + h_{m} (x, y) \times [n_{m} (x, y) - 1] \\ = O P D_{s} + O P D_{m}, \end{array}

\begin{array}{l} G_{+ 1} = \sqrt{I_{s} I_{r}} \times \exp [- | \frac{O P D_{t o t a l}}{c} | \frac{c}{l_{c}}] \times \exp [- j 2 π \frac{c}{λ} \frac{O P D_{t o t a l}}{c}] \\ = \sqrt{I_{s} I_{r}} \times \exp [- | \frac{O P D_{t o t a l}}{l_{c}} |] \times \exp [- j \frac{2 π}{λ} O P D_{t o t a l}] . \end{array}

l_{c}

G_{+ 1} = \sqrt{I_{r} I_{s}} \exp [- \frac{| O P D_{t o t a l} |}{l_{c} (x, y)}] \times \exp [- j \frac{2 π}{λ} O P D_{t o t a l}] \times \exp [- j \frac{2 π}{λ} y \sin (θ)],

Abstract

Supplementary Material (1)

Cited By

Figures (11)

Equations (11)

Optics Express