# US 11,994,470 B2 · Pixel-wise point spread function engineering systems and methods

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- Number: US 11,994,470 B2
- Document ID: US11994470B2
- Status: Granted
- Kind: B2
- Application number: 17/880,648
- Filed: 2022-08-04
- Published: 2023-02-16
- Granted: 2024-05-28
- Earliest claimed: 2021-08-03
- Assignees: Washington University
- Applicants: Washington University
- Inventors: Matthew Lew; Tingting Wu
- Web page: https://patentgrep.com/patent/US11994470B2

## CPC

- G01N 21/6458: {Fluorescence microscopy (fluorescence microscopes per se G02B21/0076 and G02B21/16)}
- G02B 21/0076: {arrangements using fluorescence or luminescence}
- G01N 21/6428: {Measuring fluorescence of fluorescent products of reactions or of fluorochrome labelled reactive substances, e.g. measuring quenching effects, using measuring "optrodes" (in vivo A61B5/00; immunoassay G01N33/53)}
- G01N 21/6445: {Measuring fluorescence polarisation}
- G01N 2021/6439: {with indicators, stains, dyes, tags, labels, marks}
- G02B 5/3083: {Birefringent or phase retarding elements (G02B5/3008, G02B5/3016 take precedence; systems for polarisation control G02B27/286; manufacturing phase modulating patterns by lithographic processes G03F7/001)}
- G02B 27/44: Grating systems; Zone plate systems (G02B27/46 takes precedence)
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS

## Abstract

Systems, devices, and methods for producing an optimized phase mask for use in a single-molecule orientation localization microscopy (SMOLM) imaging system are disclosed.

## Claims

### Claim 1

A computer-implemented method for producing an optical mask for an SMOLM imaging system, the method comprising:
a. providing, to a computing device, a baseline optical mask comprising a plurality of mask pixels distributed at a plurality of mask pixel positions within a mask plane, each mask pixel comprising at least one optical modulation element configured to modulate at least one optical parameter of a photon produced by an emitter propagating therethrough;
b. providing, to the computing device, a plurality of emitter images indicative of dipole spread functions captured using the SMOLM imaging system provided with the baseline optical mask, each image comprising a plurality of image pixels indicative of a dipole spread function, each image pixel comprising a pixel position and a pixel intensity indicative of a number of photons detected at the pixel position, wherein each emitter image is obtained for a reference emitter positioned at a reference lateral position and at one sample orientation within an orientation space;
c. determining, using the computing device, a loss function comprising a matrix quantifying variances in precision of emitter orientations estimated from the dipole spread functions from the plurality of images;
d. iteratively modifying, using the computing device, at least one optical parameter of at least one mask pixel to minimize the loss function to produce the optical mask.

### Claim 2 (depends on 1)

The method of claim 1, wherein the at least one optical parameter modulated by each mask pixel comprises a phase, a polarization, a birefringence, and any combination thereof.

### Claim 3 (depends on 2)

The method of claim 2, wherein the optical parameter modulated by each mask pixel is the phase.

### Claim 4 (depends on 1)

The method of claim 1, wherein the plurality of emitter images are obtained by:
a. imaging an emitter at a plurality of orientations within the orientation space using the SMOLM imaging system provided with a baseline optical mask or a modified optical mask; or
b. simulating each emitter image using a computational model of a SMOLM imaging system provided with a baseline optical mask or a modified optical mask.

### Claim 5 (depends on 4)

The method of claim 4 wherein each emitter image is simulated using a dipole-dipole model.

### Claim 6 (depends on 1)

The method of claim 1, wherein the matrix quantifying variances in precision of emitter orientations estimated from the dipole spread functions from the plurality of images comprises a Cramér-Rao bound matrix K, wherein the Cramér-Rao bound matrix quantifies a lower bound on a variance of estimated emitter orientations.

### Claim 7 (depends on 6)

The method of claim 6, wherein the loss function l is given by:
l
=
min
P
∑
m
∈
ℂ
K
⁡
(
P
,
m
)
wherein m is a second-moment vector m of a dipole spread function obtained using the optical mask P, and is a uniformly sampled emitter orientation space.

### Claim 8 (depends on 1)

The method of claim 1, further including producing additional optical masks for images of an emitter positioned at different axial positions within the SMOLM imaging system, for images of an emitter comprising background photons, for images of emitters positioned out of the focal plane of the SMOLM imaging system.

### Claim 9 (depends on 1)

The method in claim 1 wherein the loss function is quantified and minimized by a divergence statistical model.

### Claim 10 (depends on 1)

The method of claim 1 wherein the each emitter image of the plurality of images is indicative of at least two dipole spread functions corresponding to at least two emitters within each image.

### Claim 11

A computer-implemented method for producing a phase mask for an SMOLM imaging system, the method comprising:
a. providing, to a computing device, a baseline phase mask comprising a plurality of mask pixels distributed at a plurality of mask pixel positions within a mask plane, each mask pixel comprising a phase modulation element configured to modulate the phase of a photon produced by an emitter propagating therethrough;
b. providing, to the computing device, a plurality of emitter images indicative of dipole spread functions captured using the SMOLM imaging system provided with the baseline optical mask, each image comprising a plurality of image pixels indicative of a dipole spread function, each image pixel comprising a pixel position and a pixel intensity indicative of a number of photons detected at the pixel position, wherein each emitter image is obtained for a reference emitter positioned at a reference lateral position and at one sample orientation within an orientation space;
c. determining, using the computing device, a loss function comprising a matrix quantifying variances in precision of emitter orientations estimated from the dipole spread functions from the plurality of images;
d. iteratively modifying, using the computing device, at least one optical parameter of at least one mask pixel to minimize the loss function to produce the phase mask.

### Claim 12 (depends on 11)

The method of claim 11, wherein the plurality of emitter images are obtained by:
a. imaging an emitter at a plurality of orientations within the orientation space using the SMOLM imaging system provided with a baseline optical mask or a modified optical mask; or
b. simulating each emitter image using a computational model of a SMOLM imaging system provided with a baseline optical mask or a modified optical mask.

### Claim 13 (depends on 12)

The method of claim 12 wherein each emitter image is simulated using a dipole-dipole model.

### Claim 14 (depends on 11)

The method of claim 11, wherein the matrix quantifying variances in precision of emitter orientations estimated from the dipole spread functions from the plurality of images comprises a Cramér-Rao bound matrix K, wherein the Cramér-Rao bound matrix quantifies a lower bound on a variance of estimated emitter orientations.

### Claim 15 (depends on 14)

The method of claim 14, wherein the loss function l is given by:
l
=
min
P
∑
m
∈
ℂ
K
⁡
(
P
,
m
)
wherein m is a second-moment vector m of a dipole spread function obtained using the optical mask P, and is a uniformly sampled emitter orientation space.

### Claim 16 (depends on 11)

The method of claim 11, further including producing additional optical masks for images of an emitter positioned at different axial positions within the SMOLM imaging system, for images of an emitter comprising background photons, for images of emitters positioned out of the focal plane of the SMOLM imaging system.

### Claim 17 (depends on 11)

The method in claim 11 wherein the loss function is quantified and minimized by a divergence statistical model.

### Claim 18 (depends on 11)

The method of claim 11 wherein the each emitter image of the plurality of images is indicative of at least two dipole spread functions corresponding to at least two emitters within each image.