# Simulating MT images (notes from Feb 12 meeting)

by Steve Koch
# 1. Randomly place emitters

## 1.1. using MT lattice

### 1.1.1. Simple method is 8 nm latice with maximum of 13 per site

# 2. Each emitter produces airy disc in image plane

## 2.1. All air discs add up to form final probability density function for photon arrivals

# 3. Single-photon simulation

## 3.1. PDF in image plane can be used to randomly land photons

### 3.1.1. LJH: is the probability density function the airy disc? Bit confused

3.1.1.1. SJK: Yes, it would be the airy disc normalized so that total 2-D integral is 1.0

## 3.2. two random numbers per photon

### 3.2.1. one for radial position (distance from center)

3.2.1.1. Not sure if there is faster / better method to get this random number, besides numerical integration. Since pixel resolution is really low, there's no need to be super-accurate with this integration to form random variable, I think.

### 3.2.2. one for angular position (uniform distribution for airy disc)

### 3.2.3. This strategy was for a single airy disc, which would be radially symmetric. With what you were doing in your notebook 2/24, a different strategy would be needed.

3.2.3.1. But I think possibly you can still do this method, but a 3rd random number is needed to determine which of the emitters emitted the photon.

3.2.3.1.1. Random #1--which emitter?

3.2.3.1.2. Random #2--what angle around the emitter? (phi)

3.2.3.1.3. Random #3--how far from emitter? (r)

## 3.3. double-precision number for photon position is converted into pixel location

## 3.4. All pixels are 16-bit (or maybe even double-precision) so you can count all photons without saturating

### 3.4.1. saturation effects can be added in later if desired.

## 3.5. Starter-project for this method

### 3.5.1. A single emitter can be simulated and you can test how accurate it can be localized (by fitting to air disc or gaussian) versus number of photons collected.

3.5.1.1. A common exercise, I think for localization microscopy / single-molecule detection people.

# 4. Poisson (Gaussian) approx method

## 4.1. Actual average number of photons in an image is somehow estimated (from real data, perhaps)

## 4.2. Predict photons in oversampled (10x e.g.) image

### 4.2.1. Mean pixel value is determined by sum of airy discs (overall PDF)

4.2.1.1. multiplied by the average number of photons in entire image

### 4.2.2. noise is determined by poisson statistics

## 4.3. Convert oversampled image to 1x version