Incoherent Ptychography

PyPty supports three types of incoherent scattering:

• Probe modes: multiple coherent probes
• Object modes: multiple transmission functions
• Static background: uniform parasitic scattering

Let (O) be a coherent object and (P) a coherent probe. Define the forward model

[ FM(O, P) ],

which maps object and probe to an intensity pattern. The total measured intensity is then

[ S + \sum_{i,j} FM(O_i, P_j), ]

where:

• (S) is a static offset common to all patterns,
• (O_i) are object modes,
• (P_j) are probe modes.

Probe Modes

By default, PyPty generates a single coherent probe mode using a calibrated pypty_params dictionary. To use multiple modes, you have three options:

1. User-defined modes
   Provide an array of shape [Ny, Nx, Nmodes] or [Ny, Nx, Nmodes, Nroi] via the probe_modes key.

2. Defocus spread modes
   Set defocus_spread_modes in pypty_params to a 1D array of defocus values (in Å). PyPty applies different defocus values to generate multiple modes. This can be useful for monolayers or for samples with drift or wobble along the beam propgation direction.

3. Hermite modes
   Specify n_hermite_probe_modes: (order_x, order_y) to generate Hermite polynomials up to the given orders in the x and y directions.

Static Background

PyPty models a static incoherent offset in two ways:

1. User-defined background
   Provide static_background as a 2D array matching your diffraction pattern size (including padding).

2. Automatic initialization
   Set static_background to a float > 1E-7. PyPty will create a randomized background normalized to the total number counts specified by the provided float.

Object Modes

Reconstructing incoherent object modes requires a well-calibrated probe and accurate positions. Initialization options include:

1. User-defined modes
   Provide obj as a 4D array of shape (y, x, z, Nmodes) in pypty_params (after attached experimental parameters to the preset pypty_params).

2. Automatic initialization
   In experimental_params (before appending them to pypty_params), set:

3. num_obj_modes: integer number of object modes
4. obj_phase_sigma: standard deviation of Gaussian noise for initial phase

Ensure each mode starts from a different random seed to avoid identical updates.