# Open Source

This web site provides open datasets and source code to researchers who desire to contribute to a community of reproducible research. I am happy to share source code & data from papers and projects, as long as appropriate credit is given and it is not being used for commercial purposes. Feel free to email me (leitian AT bu DOT edu) for questions/comments.

All codes are distributed under the terms of the GNU General Public License 2.0.

## SOFTWARE

### Computational Microscopy with Coded Illumination

#### Fourier ptychography reconstruction algorithm with Quasi-Newton’s method

Matlab code implements Fourier ptychography reconstruction algorithm from a set of images captured under different illumination angles (e.g. in an LED array microscope), using either sequential or multiplexed coded illumination. The algorithm simultaneously estimates the complex object function (amplitude + phase) with high resolution (defined by objective NA+illumination NA) and the pupil function (aberrations). It implements a sequential quasi-Newton’s method with Tikhonov (L2) regularization.

**Reference:**

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomedical Optics Express 5, 2376-2389 (2014).

#### Quantitative DPC phase imaging on LED array microscope

Matlab code implements a Tikhonov deconvolution based phase reconstruction algorithm from single or multi-axis DPC data. Images should be captured with LED array illumination using two complementary asymmetric patterns (e.g. halves of the brightfield circle) on in each image. The transfer functions are calculated according to the Weak Object Transfer Function and solve for phase in the least squares sense. The complementary images are subtracted and DPC images contain the phase gradient information.

**Reference:**

Lei Tian, Laura Waller, Quantitative differential phase contrast imaging in an LED array microscope, Opt. Express 23, 11394-11403 (2015).

#### Light field refocusing and 3D differential phase contrast (DPC) on LED array microscope

Matlab code implements the popular ‘shift-and-add’ light field digital refocusing algorithm. The code is designed for processing data captured by sequentially turning on an array of illumination angles on our LED array microscope. It then splits the data based on illumination angles according to the differential phase contrast (DPC) method to compute the phase gradient information of the sample. The same algorithms can be also used for lenslet-based light field microscope.

##### Reference:

Lei Tian, et al., 3D differential phase contrast microscopy with computational illumination using an LED array, Opt. Lett. 9, 1326 – 1329 (2014).

### Phase Imaging from Defocus

#### Compressive phase tomography based on Transport of Intensity Equation (TIE)

Matlab code implements a 3D total variation (TV) based compressive reconstruction algorithm for tomographic recovery of 3D refractive index distribution for weakly attenuating objects from angularly sparsely measured data. Our model makes the projection approximation which works well for X-ray phase tomography. The operator adapts the non-uniform FFT (NUFFT) to account for radial Fourier sampling in tomography. The 3D TV-minimization is implemented by a modified TwIST algorithm.

##### Reference:

Lei Tian, et al., Compressive X-ray phase tomography based on the transport of intensity equation, Opt. Lett. 38, 3418-3421 (2013).

### Digital Holography

#### Simulation of holograms from particle clouds based on Mie scattering theory

Matlab code simulates in-line (Gabor) holograms from 3D distributions of dielectric particles. The code makes the 1st Born approximation, which only accounts for single scatterings from particles but not higher order wave optic interactions. The total scattered field is calculated as the linear sum from the scattered fields from each particles. The Mie scattering calculation is adapted from the work of Christian Maetzler.

##### Reference:

Lei Tian, Chapter 2 of my thesis “Compressive phase retrieval“, MIT 2013.

W. Chen, et. al, Empirical concentration bounds for compressive holographic bubble imaging based on a Mie scattering model, Opt. Express 23, 4715-4725 (2015)

## DATASETS

### Computational Microscopy with Coded Illumination

#### Fourier ptychographic microscopy (FPM) on LED array microscope

Dataset contains images captured from two different LED patterning methods (sequential and randomly multiplexed) within 0.5 illumination NA, from a 4x objective. In our paper, we achieved resolution corresponding to the sum of the two NAs~0.6, using a new FPM algorithms based on alternating projection with a modified Newton’s method. The setup uses an LED array (e.g. Adafruit) placed at ~60 – 70mm above the sample on a Nikon TE300 microscope. Details on experiments are listed in a separate text file included.

Dataset 1: stained histology slide, our reconstruction is here

Dataset 2: USAF resolution target

FAQs:

- If you have trouble in reading in the images in the proper order (1,2,3, …) , try this Natural-Order Filename Sort.

##### Reference:

Lei Tian, et al., Multiplexed coded illumination for Fourier Ptychography with an LED array microscope, Biomed. Opt. Express 5, 2376-2389 (2014).

#### Quantitative Phase Imaging using FPM on LED array microscope

FPM also enables label-free quantitative phase imaging capability. Datasets contain images captured from unstained fixed and live cell cultures.

Dataset 1: in vitro Hela cell culture

Dataset 2: fixed stained and unstained U2OS cell sample, our reconstruction is here

##### Reference:

Lei Tian, et al. Computational illumination for high-speed in vitro Fourier ptychographic microscopy, Optica 2, 904-911 (2015).

#### 3D Fourier ptychography on LED array microscope

Dataset contains images captured from sequential LED illumination up to 0.41 NA, using a 4x objective (0.1 NA). In our paper, we achieved resolution corresponding to the sum of the two NAs~0.5. Our 3D FPM algorithms is based on multislice model that accounts for multiple scattering effects from 3D model. It combines 3D light field refocusing with FPM to achieve super resolution in both lateral (x,y) and axial (z) dimensions across a large field of view.

Dataset 1: two stacked resolution targets separated by ~100um

Dataset 2: Spiral Algea

##### Reference:

Lei Tian, Laura Waller, 3D intensity and phase imaging from light field measurements in an LED array microscope, Optica 2, 104-111 (2015).