FPM glossary

These short definitions are for readers who are comfortable with Python and NumPy but new to physical optics. Follow each link for the implementation's units, signs, and discrete-array conventions.

Numerical aperture (NA)

A dimensionless measure of the angular range admitted by an optical system. In fpm-rs, objective_na sets the radius of the objective's circular Fourier passband. A larger value passes higher transverse spatial frequencies. See Object, pupil, and Fourier sampling.

Synthetic NA

A summary of the largest Fourier radius reached by combining the objective passband with shifted illumination. fpm-rs records it as objective_na plus the largest illumination NA. It is useful for estimating resolution, but it does not prove that the enclosed Fourier region is filled or recoverable. See Low-resolution frames and the reconstruction grid.

Pupil function

A complex-valued Fourier-space transfer function for the objective. Its magnitude describes transmitted spatial frequencies; its phase carries defocus and other modeled aberrations. Multiplying an object-spectrum crop by the pupil produces the field that is propagated to a detector frame. See Object, pupil, and Fourier sampling.

k-vector

A wave-propagation vector expressed as angular spatial frequency. fpm-rs stores the transverse pair (kx, ky) in radians per metre. During model compilation, that pair selects the location of a low-resolution crop in the centered high-resolution object spectrum. See Object, pupil, and Fourier sampling.

Bright-field and dark-field illumination

A source is bright-field when its unscattered illumination lies inside the objective passband; its illumination NA is no greater than the objective NA. A source outside that passband is dark-field, so an unscattered field would not reach the detector through the ideal pupil. Dark-field frames can still carry specimen-scattered information. See Object, pupil, and Fourier sampling.

Bright-field circle initialization

A pre-reconstruction estimate of planar-array geometry from the circular pupil edges visible in Fourier transforms of suitable bright-field intensity images. In fpm-rs, detected centers are fitted to physical pose, pitch, or reference-index variables; they are not stored as arbitrary per-source shifts. The method needs textured, single-source, all-valid frames and is not interchangeable with measurement-loss calibration. See Bright-field planar-array initialization.

LED pitch

The centre-to-centre spacing of neighboring LEDs in a planar array. fpm-rs stores pitch_m in metres as (pitch_x, pitch_y) after accepting either a scalar equal pitch or a two-value input. Pitch is separate from the array's pose and reference index. See Illumination architecture, units, and acquisition.

Defocus

Axial displacement from the modeled focus. fpm-rs expresses defocus_distance in metres and compiles it as a spatial-frequency-dependent phase in the pupil, rather than shifting image pixels. See Object, pupil, and Fourier sampling.

The Fourier-crop interpretation follows G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nature Photonics 7, 739–745 (2013). The joint object/pupil interpretation follows X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Optics Express 22(5), 4960–4972 (2014).