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Basics

Determining Lens Properties

Retrieve EFL, F/#, pupil positions, cardinal points, and paraxial ray data from an optical system.

BeginnerBasicsNumPy backend8 min read

Introduction

This tutorial shows how to inspect the main first-order properties of a lens in Optiland using the built-in Cooke Triplet sample. You will retrieve focal quantities, principal and nodal plane locations, pupil diameters and positions, the optical invariant, and the paraxial marginal and chief rays.

By the end, you will know where to look in the lens.paraxial interface when you need quick optical diagnostics without moving to full ray analysis.

Core concepts used

CookeTriplet()
A built-in sample objective that is convenient for demonstrations and regression examples.
lens.paraxial.f2()
Returns the effective focal length of the optical system.
lens.paraxial.EPD()
Returns the entrance pupil diameter.
lens.paraxial.FNO()
Returns the image-space F-number.
lens.paraxial.marginal_ray()
Returns the paraxial marginal ray height and slope at each surface.

Step-by-step walkthrough

1

Load and preview the Cooke Triplet

Import the built-in Cooke Triplet sample, instantiate it, and draw the layout to establish a geometric picture of the lens before reading its first-order properties.

python
from optiland.samples.objectives import CookeTriplet

lens = CookeTriplet()
lens.draw()
Cooke Triplet optical layout
2

Read focal, principal, and nodal data

Query the most common cardinal-point quantities, including front and back focal lengths, focal points, principal planes, and nodal planes.

python
print(f"Front focal length: {lens.paraxial.f1():.1f} mm")
print(f"Focal length: {lens.paraxial.f2():.1f} mm")
print(f"Front focal point: {lens.paraxial.F1():.1f} mm")
print(f"Back focal point: {lens.paraxial.F2():.1f} mm")
print(f"Front principal plane: {lens.paraxial.P1():.1f} mm")
print(f"Back principal plane: {lens.paraxial.P2():.1f} mm")
print(f"Front nodal plane: {lens.paraxial.N1():.1f} mm")
print(f"Back nodal plane: {lens.paraxial.N2():.1f} mm")
3

Measure entrance and exit pupil diameters

For object-space quantities, Optiland measures positions relative to the first lens surface. Image-space quantities are measured relative to the image surface.

python
print(f"Entrance pupil diameter: {lens.paraxial.EPD():.1f} mm")
print(f"Exit pupil diameter: {lens.paraxial.XPD():.1f} mm")
4

Measure entrance and exit pupil locations

After checking pupil sizes, retrieve the longitudinal locations of the entrance and exit pupils.

python
print(f"Entrance pupil position: {lens.paraxial.EPL():.1f} mm")
print(f"Exit pupil position: {lens.paraxial.XPL():.1f} mm")
5

Compute F-number, magnification, and invariant

Magnification is usually most meaningful for finite-conjugate systems, but it is included here as a simple illustration alongside the image-space F-number and optical invariant.

python
print(f"Image-space F-Number: {lens.paraxial.FNO():.1f}")
print(f"Magnification: {lens.paraxial.magnification():.1f}")
print(f"Invariant: {lens.paraxial.invariant():.3f}")
6

Inspect the marginal ray across the system

Print the paraxial marginal ray height and slope at each surface to see how the edge-of-aperture ray evolves through the lens.

python
print("Marginal Ray: ")

ya, ua = lens.paraxial.marginal_ray()
for k in range(len(ya)):
    print(f"\tSurface {k}: y = {ya[k, 0]:.3f}, u = {ua[k, 0]:.3f}")
7

Inspect the chief ray across the system

Finally, print the paraxial chief ray height and slope at each surface to understand how the field ray propagates through the system.

python
print("Chief Ray: ")

yb, ub = lens.paraxial.chief_ray()
for k in range(len(yb)):
    print(f"\tSurface {k}: y = {yb[k, 0]:.3f}, u = {ub[k, 0]:.3f}")
Show full code listing
python
from optiland.samples.objectives import CookeTriplet

lens = CookeTriplet()

lens.draw()

print(f"Front focal length: {lens.paraxial.f1():.1f} mm")
print(f"Focal length: {lens.paraxial.f2():.1f} mm")
print(f"Front focal point: {lens.paraxial.F1():.1f} mm")
print(f"Back focal point: {lens.paraxial.F2():.1f} mm")
print(f"Front principal plane: {lens.paraxial.P1():.1f} mm")
print(f"Back principal plane: {lens.paraxial.P2():.1f} mm")
print(f"Front nodal plane: {lens.paraxial.N1():.1f} mm")
print(f"Back nodal plane: {lens.paraxial.N2():.1f} mm")

print(f"Entrance pupil diameter: {lens.paraxial.EPD():.1f} mm")
print(f"Exit pupil diameter: {lens.paraxial.XPD():.1f} mm")

print(f"Entrance pupil position: {lens.paraxial.EPL():.1f} mm")
print(f"Exit pupil position: {lens.paraxial.XPL():.1f} mm")

print(f"Image-space F-Number: {lens.paraxial.FNO():.1f}")
print(f"Magnification: {lens.paraxial.magnification():.1f}")
print(f"Invariant: {lens.paraxial.invariant():.3f}")

print("Marginal Ray: ")

ya, ua = lens.paraxial.marginal_ray()
for k in range(len(ya)):
    print(f"\tSurface {k}: y = {ya[k, 0]:.3f}, u = {ua[k, 0]:.3f}")

print("Chief Ray: ")

yb, ub = lens.paraxial.chief_ray()
for k in range(len(yb)):
    print(f"\tSurface {k}: y = {yb[k, 0]:.3f}, u = {ub[k, 0]:.3f}")

Conclusions

The paraxial interface gives a compact first-order summary of an optical system: focal properties, pupil data, cardinal planes, and paraxial ray behavior. This makes it a useful entry point when you want to inspect a design quickly before moving to full tracing, aberration analysis, or optimization.

Next tutorials

NextSaving and Loading Optiland FilesSerialize your optical systems to disk for later use or sharing.RelatedTracing and Analyzing RaysMove beyond paraxial optics to real, non-linear ray tracing.

Original notebook: Tutorial_1b_Lens_Properties.ipynb on GitHub · ReadTheDocs