CASS microscopy

This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (March 2022) (Learn how and when to remove this template message)

|

CASS is an acronym of Collective Accumulation of Single Scattering. This technique collects faint single scattering signal among the intense multiple scattering background in biological sample, thereby enabling conventional diffraction-limited imaging of a target embedded in a turbid sample.

## Contents

* 1 Principle
* 1.1 Input-Output Relationship for a given Object Function
* 1.2 Coherent Addition
* 2 Comparison to Confocal Microscopy
* 3 Application
* 3.1 Rat brain imaging through skull
* 4 References

## Principle

CASS microscopy makes use of time-gated detection and spatial input-output wave correlation. Theoretical description is given below.

### Input-Output Relationship for a given Object Function

Let O(𝐫) be a planar object function that we wish to reconstruct. Then, it is related to its Fourier transform O~(𝐤s) by

O(𝐫)=∫O~(𝐤s)ei𝐤s⋅𝐫d𝐤s

where 𝐤s represents a 2-dimensional wavevector.

Now, let's take a look at the relation between input and output wave in reflection geometry.

Eo(𝐫)=O(𝐫)Ei(𝐫)=O(𝐫)ei𝐤i⋅𝐫

where we assumed the incoming wave is plane wave.

Then, the angular spectrum of the output field with given input field is

E~o(𝐤o,𝐤i)=∫Eo(𝐫o;𝐤i)ei𝐤o⋅𝐫od𝐫o=O~(𝐤o−𝐤i)

where Eo(𝐫o;𝐤i)=O(𝐫o)ei𝐤i⋅𝐫o=∫O~(𝐤s)ei(𝐤i+𝐤s)⋅𝐫od𝐤s has been used.

### Coherent Addition

Now, consider a reflection matrix in wavevector space without aberration.

E~o(𝐤o;𝐤i)=γO~(𝐤o−𝐤i)+βE~M(𝐤o;𝐤i)

where γ(z)=exp⁡(−2z/ls) explains the attenuation of single-scattered wave, and β explains the attenuation of the time-gated multiple-scattered waves.

With Δ𝐤≡𝐤o−𝐤i, total summation of output field over all possible input wavevector becomes:

E~CASS(Δ𝐤)=∑kiNE~(Δ𝐤+𝐤i;𝐤i)=NγO~(Δ𝐤)+∑kiNβE~(Δ𝐤+𝐤i;𝐤i)

from which we observe that single-scattered field adds up coherently with the increasing number of incoming wavevectors, whereas the multiple-scattered field adds up incoherently.

Accordingly, the output intensity behaves as follows with the number of incoming wavevector N[1]

ICASS∼γN2|O~(Δ𝐤)|2+βN

[2]

## Comparison to Confocal Microscopy

CASS microscopy has a lot in common with confocal microscopy which enables optical sectioning by eliminating scattered light from other planes by using a confocal pinhole. The main difference between these two-microscopy modality comes from whether the basis of illumination is in position space or in momentum space. So, let us try to understand the principle of confocal microscopy in terms of momentum basis, here.

In confocal microscopy, the effect of the pinhole can be understood by the condition that A(𝐤i)ei𝐤i⋅𝐫c=1 for all possible input wavevector 𝐤i's, where it is assumed that illumination is focused at 𝐫=𝐫c.

The resulting field from confocal microscopy (CM) then becomes

ECM(𝐫o)=∑𝐤iNEo(𝐫o;𝐤i)=∑𝐤iA(𝐤i)ei𝐤i⋅𝐫oO(𝐫o)=∑𝐤iei𝐤i⋅(𝐫o−𝐫c)O(𝐫o)

where N refers to the number of possible input wavevector 𝐤i's.

The formula above gives ECM(𝐫o)=N⋅O(𝐫c) for the case of 𝐫o=𝐫c.

## Application

### Rat brain imaging through skull

CASS microscopy has been used to image rat brain without removing skull. It has been further developed such that light energy can be delivered on the target beneath the skull by using reflection eigenchannel, and about 10-fold increase in light energy delivery has been reported.[3]

## References

1. ↑ Kang, Sungsam; Jeong, Seungwon; Choi, Wonjun; Ko, Hakseok; Yang, Taeseok D.; Joo, Jang Ho; Lee, Jae-Seung; Lim, Yong-Sik et al. (April 2015). "Imaging deep within a scattering medium using collective accumulation of single-scattered waves". Nature Photonics 9 (4): 253–258. doi:10.1038/nphoton.2015.24. Bibcode: 2015NaPho...9..253K.
2. ↑ Kang, Pilsung; Kang, Sungsam; Jo, Yonghyeon; Ko, Hakseok; Kim, Guanghoon; Lee, Ye-Ryoung; Choi, Wonshik (1 February 2021). "Optical transfer function of time-gated coherent imaging in the presence of a scattering medium". Optics Express 29 (3): 3395–3405. doi:10.1364/OE.412988. PMID 33770938. Bibcode: 2021OExpr..29.3395K.
3. ↑ Jeong, Seungwon; Lee, Ye-Ryoung; Choi, Wonjun; Kang, Sungsam; Hong, Jin Hee; Park, Jin-Sung; Lim, Yong-Sik; Park, Hong-Gyu et al. (May 2018). "Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering". Nature Photonics 12 (5): 277–283. doi:10.1038/s41566-018-0120-9. Bibcode: 2018NaPho..12..277J.

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/CASS microscopy. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Physics:CASS_microscopy&oldid=4108486"