Better Initialization

[allevitan]

I think it would make a big difference to beamline users if it's possible to automatically correct an initial probe guess for differences in propagation state, photon energy, and detector distance. I think it's worth expanding some fucntions in tools.initializers and writing a special function for fancy_ptycho to do it from a saved result

[allevitan]

I think it should work this way:

• Step 1: propagate the initial probe to focus, using either an angular-spectrum propagator (for far-field ptycho or genuine near-field ptycho) or a Fresnel propagator (for near-field ptycho with the Fresnel scaling theorem). The default propagation distance should be either loaded from the geometry information for near-field ptycho, or an assumption that the beam is at focus otherwise.
• Step 2: Adjust the pixel size with a crop and pad step to match the pixel size corresponding to the new detector position and energy, using the far-field equations for pixel size (for either a new model with far-field ptycho or Fresnel-scaling-theorem near-field) or the detector pixel size (for genuine near-field). This could potentially include a 3-Fourier-transform scaling step if we want to get fancy for subpixel accuracy).
• Step 3: Propagate the probe back to the assumed initial state for the new model, using the same rules as step 1 but now for the new model's experiment type.

This would flexibly allow for:

• Changes in detector position and crop
• Changes in photon energy
• Changes in propagation state
• Swaps between model types (e.g. using a far-field ptycho scan to initialize a near-field ptycho scan after defocusing).