The datasets store both motion and observation information of a single fluorescent sub-diffraction limit-sized particle moving in a three-dimensional confined environment. The confined motion is following a nonlinear model driven by non-Gaussian noise, the observation is formed by engineered Double-helix (DH) point spread function (PSF) and captured by scientific complementary metal-oxide semiconductor (sCMOS) camera. Based on our prior computationally efficient application of Sequential Monte Carlo - Expectation Maximization (SMC-EM), we extended it to handle the DH-PSF for encoding the three-dimensional position of the particle in two-dimensional image plane of the camera. We focus on studying the datasets at low signal and low signal-to-background ratio (SBR). Based on the datasets across different SBR and confinement lengths, a quantitative comparison is conducted to show that in the low signal regime, the SMC-EM approach outperforms the other methods while at higher signal-to-background levels, SMC-EM and the MLE-based methods perform equally well and both are significantly better than fitting to the MSD. In addition, our results indicate that at smaller confinement lengths where the nonlinearities dominate the motion model, the SMC-EM approach is superior to the alternative approaches.

All datasets were simulated using Python 3.8. The camera type considered in this work is the scientific complementary metal-oxide semiconductor (sCMOS) where both shot noise and the pixel-dependent readout noise are common noise sources. The motion of a single fluorescent particle was generated at a time step of 1 ms. The camera was assumed to take images at a rate of 10 Hz with a shutter period of 10 ms. Motion blur is considered for all data simulation. The 10 pixelated images during the shutter period were accumulated to generate a single camera image. (See the Usage Notes for details).

* DATA-SPECIFIC INFORMATION FOR: [data_by_sCMOS_dh.zip]

1. Images were captured by sCMOS, integrating the DH-PSF.
2. All images are in the local region of 15-by-15 pixels.
3. The background noise is 10 counts, while the signal level ranges from 10 to 50.
4. The confinement length in three dimensions ranges from 0.1 μm to 0.5 μm.
5. For each optical settings, 50 datasets were simulated (counted from 0 to 49).
6. Taking the sub-folder [sCMOS_N10G10Image100D0.01L0.1_double_helix] as an example, the details are as follows:

(1). Background noise N=10, signal level G=10, number of images per dataset =100, diffusion coefficient D=0.01 μm²/s, confinement length L=0.1 μm;

(2). Inside the sub-folder [sCMOS_N10G10Image100D0.01L0.1_double_helix], the detailed description of the files for the 0^th dataset is as follows:

• • [local_sigma_0.csv] row*column=100*225; where row denotes the time steps, column denotes the pixel. Each pixel contains information of "sigma" characterizing the readout noise of the Hamamatsu ORCA Flash 4.0 camera.
  • [photon_observation_0.csv] row*column=225*100; where the simulated images in each column containing a single image, organized sequentially from the initial time down to the final time. The 225 entries in each row are the photon counts from the 15-by-15 pixeled array, organized starting from the top-left pixel, going horizontally across the top five pixels, and continuing to the bottom right pixel.
  • [sensor_position_0.csv] row*column=100*2; In generating images, we assumed segmentation of the full camera image was done previously and thus the location of the 15-by-15 array of pixels may change at each time step. This data gives the position of the pixel array starting from the initial time down to the final time, with the first column corresponding to the x-coordinate and the second column to the y-coordinate.
  • [x_ground_truth_0.csv] row*column=1*100; where the entire row contains the true location of the particle in the x-direction at each time step. The data is organized starting with the first timestep and proceeding down to the last.
  • [y_ground_truth_0.csv] row*column=1*100; where the entire row contains the true location of the particle in the y-direction at each time step. The data is organized as [x_ground_truth_0.csv].
  • [z_ground_truth_0.csv] row*column=1*100; where the entire row contains the true location of the particle in the z-direction at each time step. The data is organized as [x_ground_truth_0.csv].

* DATA-SPECIFIC INFORMATION FOR: [data_for_figures_BOE.zip]

The data underlying the figures in the paper “Ye Lin, Fatemeh Sharifi and Sean B. Andersson. Three dimensional localization refinement and motion model parameter estimation for confined single particle tracking under low-light conditions. Biomedical Optics Express (2021).”