prysm.thinlens

A collection of thin lens equations for system modeling.

prysm.thinlens.object_to_image_dist(efl, object_distance)

Compute the image distance from the object distance.

Parameters:

• efl (float) – focal length of the lens

• object_distance (float or numpy.ndarray) – distance from the object to the front principal plane of the lens, negative for an object to the left of the lens

Returns:

image distance. Distance from rear principal plane (assumed to be in contact with front principal plane) to image.

Return type:

float

Notes

efl and object distance should be in the same units. Return value will be in the same units as the inputs.

prysm.thinlens.image_to_object_dist(efl, image_distance)

Compute the object distance from the image distance.

Parameters:

• efl (float) – focal length of the lens

• image_distance (float or numpy.ndarray) – distance from the object to the front principal plane of the lens, positive for an object in front of a lens of positive focal length.

Notes

efl and image distance should be in the same units. Return value will be in the same units as the input.

prysm.thinlens.image_dist_epd_to_na(image_distance, epd)

Compute the NA from an image distance and entrance pupil diameter.

Parameters:

• image_distance (float) – distance from the image to the entrance pupil

• epd (float) – diameter of the entrance pupil

Returns:

numerical aperture. The NA of the system.

Return type:

float

prysm.thinlens.image_dist_epd_to_fno(image_distance, epd)

Compute the f/# from an image distance and entrance pupil diameter.

Parameters:

• image_distance (float) – distance from the image to the entrance pupil

• epd (float) – diameter of the entrance pupil

Returns:

fno. The working f/# of the system.

Return type:

float

prysm.thinlens.fno_to_na(fno)

Convert an fno to an NA.

Parameters:

fno (float) – focal ratio

Returns:

NA. The NA of the system.

Return type:

float

prysm.thinlens.na_to_fno(na)

Convert an NA to an f/#.

Parameters:

na (float) – numerical aperture

Returns:

fno. The f/# of the system.

Return type:

float

prysm.thinlens.object_dist_to_mag(efl, object_dist)

Compute the linear magnification from the object distance and focal length.

Parameters:

• efl (float) – focal length of the lens

• object_dist (float) – object distance

Returns:

linear magnification. Also known as the lateral magnification

Return type:

float

prysm.thinlens.mag_to_object_dist(efl, mag)

Compute the object distance for a given focal length and magnification.

Parameters:

• efl (float) – focal length of the lens

• mag (float) – signed magnification

Returns:

object distance

Return type:

float

prysm.thinlens.linear_to_long_mag(lateral_mag)

Compute the longitudinal (along optical axis) magnification from the lateral mag.

Parameters:

lateral_mag (float) – linear magnification, from thin lens formulas

Returns:

longitudinal magnification

Return type:

float

prysm.thinlens.mag_to_fno(mag, infinite_fno, pupil_mag=1)

Compute the working f/# from the magnification and infinite f/#.

Parameters:

• mag (float or numpy.ndarray) – linear or lateral magnification

• infinite_fno (float) – f/# as defined by EFL/EPD

• pupil_mag (float) – pupil magnification

Returns:

working f/number

Return type:

float

prysm.thinlens.defocus_to_image_displacement(W020, fno, wavelength=None)

Compute image displacment from wavefront defocus expressed in waves 0-P to.

Parameters:

• W020 (float or numpy.ndarray) – wavefront defocus, units of waves if wavelength != None, else units of length

• fno (float) – f/# of the lens or system

• wavelength (float, optional) – wavelength of light, if None W020 takes units of length

Returns:

image displacement. Motion of image in um caused by defocus OPD

Return type:

float

prysm.thinlens.image_displacement_to_defocus(dz, fno, wavelength=None)

Compute the wavefront defocus from image shift, expressed in the same units as the shift.

Parameters:

• dz (float or numpy.ndarray) – displacement of the image

• fno (float) – f/# of the lens or system

• wavelength (float, optional) – wavelength of light, if None return has units the same as dz, else waves

Returns:

wavefront defocus, waves if Wavelength != None, else same units as dz

Return type:

float

prysm.thinlens.singlet_efl(c1, c2, t, n, n_ambient=1.0)

EFL of a singlet.

Parameters:

• c1 (float) – curvature of S1

• c2 (float) – curvature of S2

• t (float) – vertex-to-vertex thickness

• n (float) – refractive index

• n_ambient (float) – refractive index of the ambient medium (“air”)

Returns:

EFL

Return type:

float

prysm.thinlens.twolens_efl(efl1, efl2, separation)

Use thick lens equations to compute the focal length for two elements separated by some distance.

Parameters:

• efl1 (float) – EFL of the first lens

• efl2 (float) – EFL of the second lens

• separation (float) – separation of the two lenses

Returns:

focal length of the two lens system

Return type:

float

prysm.thinlens.twolens_bfl(efl1, efl2, separation)

Use thick lens equations to compute the back focal length for two elements separated by some distance.

Parameters:

• efl1 (float) – EFL of the first lens

• efl2 (float) – EFL of the second lens

• separation (float) – separation of the two lenses.

Returns:

back focal length of the two lens system.

Return type:

float