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Non-interferometric phase retrieval using refractive index manipulation

View Article: PubMed Central - PubMed

ABSTRACT

We present a novel, inexpensive and non-interferometric technique to retrieve phase images by using a liquid crystal phase shifter without including any physically moving parts. First, we derive a new equation of the intensity-phase relation with respect to the change of refractive index, which is similar to the transport of the intensity equation. The equation indicates that this technique is unneeded to consider the variation of magnifications between optical images. For proof of the concept, we use a liquid crystal mixture MLC 2144 to manufacture a phase shifter and to capture the optical images in a rapid succession by electrically tuning the applied voltage of the phase shifter. Experimental results demonstrate that this technique is capable of reconstructing high-resolution phase images and to realize the thickness profile of a microlens array quantitatively.

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(a) The ideal phase distribution, (b) the intensity image with noise, (c) RMS error as a function of Δn in this TIE imaging, (d) phase reconstruction for Δn = 0.2, (e) phase error distribution for Δn = 0.2, (f) phase reconstruction for Δn = 0.6 and (g) phase error distribution for Δn = 0.6.
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f4: (a) The ideal phase distribution, (b) the intensity image with noise, (c) RMS error as a function of Δn in this TIE imaging, (d) phase reconstruction for Δn = 0.2, (e) phase error distribution for Δn = 0.2, (f) phase reconstruction for Δn = 0.6 and (g) phase error distribution for Δn = 0.6.

Mentions: Equation (6) is similar to the TIE, and we use FD methods to approximate the derivative by using two images. As a result, an optimal choice of Δn is necessary in order to avoid unwanted nonlinearity error and the noisy phase reconstructions1325. In simulations, a phase specimen with a Gaussian profile is used, as shown in Fig. 4(a). The incident wavelength is 633 nm and the length of the phase shifter is 50 μm. A 1% white Gaussian noise is added to each intensity image, as shown in Fig. 4(b). Figure 4(c) shows the root-mean-squared (RMS) error in phase construction as a function of Δn. We can see that minimal RMS is obtained as Δn is approximately 0.2. The corresponding optical path difference for this refractive index variation is 10 μm. This optical path difference nearly equals to the optimal Δz for the conventional TIE method using mechanical translation22. Furthermore, to have a signal to noise larger than 10, the cell thickness may be further reduced to several μm based on the results in Fig. 2(b).


Non-interferometric phase retrieval using refractive index manipulation
(a) The ideal phase distribution, (b) the intensity image with noise, (c) RMS error as a function of Δn in this TIE imaging, (d) phase reconstruction for Δn = 0.2, (e) phase error distribution for Δn = 0.2, (f) phase reconstruction for Δn = 0.6 and (g) phase error distribution for Δn = 0.6.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5384217&req=5

f4: (a) The ideal phase distribution, (b) the intensity image with noise, (c) RMS error as a function of Δn in this TIE imaging, (d) phase reconstruction for Δn = 0.2, (e) phase error distribution for Δn = 0.2, (f) phase reconstruction for Δn = 0.6 and (g) phase error distribution for Δn = 0.6.
Mentions: Equation (6) is similar to the TIE, and we use FD methods to approximate the derivative by using two images. As a result, an optimal choice of Δn is necessary in order to avoid unwanted nonlinearity error and the noisy phase reconstructions1325. In simulations, a phase specimen with a Gaussian profile is used, as shown in Fig. 4(a). The incident wavelength is 633 nm and the length of the phase shifter is 50 μm. A 1% white Gaussian noise is added to each intensity image, as shown in Fig. 4(b). Figure 4(c) shows the root-mean-squared (RMS) error in phase construction as a function of Δn. We can see that minimal RMS is obtained as Δn is approximately 0.2. The corresponding optical path difference for this refractive index variation is 10 μm. This optical path difference nearly equals to the optimal Δz for the conventional TIE method using mechanical translation22. Furthermore, to have a signal to noise larger than 10, the cell thickness may be further reduced to several μm based on the results in Fig. 2(b).

View Article: PubMed Central - PubMed

ABSTRACT

We present a novel, inexpensive and non-interferometric technique to retrieve phase images by using a liquid crystal phase shifter without including any physically moving parts. First, we derive a new equation of the intensity-phase relation with respect to the change of refractive index, which is similar to the transport of the intensity equation. The equation indicates that this technique is unneeded to consider the variation of magnifications between optical images. For proof of the concept, we use a liquid crystal mixture MLC 2144 to manufacture a phase shifter and to capture the optical images in a rapid succession by electrically tuning the applied voltage of the phase shifter. Experimental results demonstrate that this technique is capable of reconstructing high-resolution phase images and to realize the thickness profile of a microlens array quantitatively.

No MeSH data available.