Ray Tracing Calculator

Calculator Inputs

Example Data Table

Example: air propagation, thin lens, then propagation. Values are illustrative.

Formula Used

This calculator uses paraxial (small-angle) ray transfer matrices with the ray vector [ y ; u ], where y is ray height (mm) and u = n*theta is reduced angle (index times angle in radians).

• Propagation through thickness t in index n: [1 t/n; 0 1]
• Thin lens with focal length f: [1 0; -1/f 1]
• Spherical refraction surface from n1 to n2 with radius R: u2 = u1 + ((n1-n2)/R)*y

Keep distances in millimeters and angles in degrees for input.

How to Use This Calculator

1. Enter the initial ray height, angle, and starting refractive index.
2. Enable elements in order and select each element type.
3. Provide parameters: thickness and index for propagation, focal length for lenses.
4. For surfaces, provide n1, n2, and radius R using one sign convention.
5. Optionally set an aperture radius to flag clipping at each element.
6. Press Calculate to see results above the form and below the header.
7. Download CSV or PDF for reports and documentation.

Professional Article

1) Purpose of Paraxial Ray Tracing

Paraxial ray tracing predicts how small-angle rays move through an optical train using simple linear updates. It is widely used in early-stage lens layout because it can estimate image formation, beam steering, and focus shifts without full geometric ray tracing. The method is fast and transparent.

2) Ray Vector and Unit Discipline

This calculator uses the state vector [y; u], where y is the ray height in millimeters and u = n·θ is the reduced angle. Here θ is the ray angle in radians and n is the refractive index. Keeping distances in millimeters makes the step table easy to audit and export.

3) Translation Through Uniform Media

In a uniform medium, the reduced angle u stays constant while the height advances by y₂ = y₁ + (t/n)·u. A 40 mm segment in air (n≈1.000) moves the ray more than the same segment in glass (n≈1.50) because the (t/n) factor is smaller in higher-index materials.

4) Thin Lens Action and Focal Length

A thin lens changes direction but not position at its plane. The update u₂ = u₁ − (1/f)·y implements the standard paraxial lens matrix. A +50 mm lens produces a stronger angular change than a +200 mm lens for the same ray height, which helps quantify focusing power.

5) Curved Interface Refraction

For a spherical refraction surface, the calculator applies u₂ = u₁ + ((n₁−n₂)/R)·y and then sets the running index to n₂. The sign of R matters: positive R means the center of curvature is to the right. A surface that transitions 1.00→1.50 with R=+80 mm typically bends rays toward the axis.

6) Apertures, Clear Radius, and Clipping

Real optics have finite clear apertures. Enter an aperture radius (mm) to flag clipping when |y| exceeds that radius at an element. This is useful for quick tolerance checks: if multiple steps show “Clipped”, consider reducing ray height, increasing aperture, or changing element spacing.

7) Reading the Step Table Like a Debug Log

The step table lists n before and after, plus y and θ in degrees. Large jumps in θ after a lens or surface are expected, but large jumps during propagation can indicate a parameter mistake. Exporting to CSV lets you chart y and θ versus step for documentation and reviews.

8) Practical Use Cases and Known Limits

Paraxial tracing is ideal for thin lenses, small angles, and near-axis rays. It supports quick estimates of focus shifts, beam steering, and axis-crossing distance z = −y/θ. It does not model large-angle aberrations, pupil walk, or thick-element geometry, so use it as a design starting point.

FAQs

1) What does “paraxial” mean in this calculator?

Paraxial means angles are small enough that linear approximations apply. The calculator uses ray matrices, where the reduced angle u = n·θ captures refraction and propagation efficiently.

2) Why does propagation use t/n instead of t?

With the [y; u] vector, translation becomes y₂ = y₁ + (t/n)·u. Higher refractive index reduces the height change for the same distance and reduced angle.

3) How should I choose the sign of R for a surface?

Use one consistent convention. Here, +R means the center of curvature lies to the right of the surface. If your results look inverted, your R sign is the first thing to verify.

4) Can I model multiple lenses and gaps?

Yes. Enable elements in order and mix propagation segments with lenses or surfaces. The step table shows the ray state after each element, making long trains easy to validate.

5) What does “Axis crossing z” represent?

It is the distance from the final plane where the ray would cross the optical axis, estimated as z = −y·n/u (equivalently −y/θ). It is most meaningful when θ is not near zero.

6) Why is a ray marked “Clipped”?

If you set an aperture radius and the computed height magnitude exceeds it at that element, the calculator flags clipping. This helps identify vignetting or clear-aperture issues early.

7) Does this replace full geometric ray tracing software?

No. It provides fast first-order estimates for near-axis performance. For large angles, thick elements, and aberrations, you should validate with full ray tracing or optical design tools.