Dial in alignment before you chase stray fringes. Model offsets, angles, mirrors, and distances accurately. See corrections instantly and document every alignment session clearly.
This tool models how initial offsets and angular errors produce a beam position error at a target. For a propagation distance L, the target-plane offsets are:
The small-angle form (use only when angles are small) replaces tan(a) with a:
Units: distance is converted to meters, offsets to millimeters, and angles to radians internally.
Optical benches behave like long lever arms: a small angular error at the source becomes a measurable spot shift at the target. For example, a 0.5 mrad tilt over 1.0 m produces roughly 0.5 mm of lateral motion, enough to clip apertures and reduce coupling. This calculator turns those relationships into fast, repeatable checks that support daily lab work and production setups.
Two effects add together at the measurement plane. The initial offset (x0, y0) represents translation at the reference plane, such as a displaced fiber collimator or a kinematic mount shift. The angular terms (θx, θy) represent tilt, such as yaw or pitch of a mirror or lens cell. The total offset at the target is the sum of translation and the propagated angle contribution.
Longer distances amplify angular errors. When you increase L, you increase sensitivity to tilt without changing the instrument. This is why alignment is often verified at a far screen or through a long beam path. In the calculator, L is converted to millimeters internally, so the output stays in mm for easy comparison to reticle scales and camera pixel calibration.
A mirror doubles angular deviation in a single reflection, so the multiplier is commonly set to 2 for steering mirrors. Double-pass systems can introduce additional factors depending on geometry. The multiplier parameter lets you model the effective angular impact without rewriting the setup. Use conservative values when multiple reflections contribute to the same axis.
The exact model uses tan(mult·θ). For very small angles, tan(a) ≈ a, which is convenient and often accurate. However, as angles grow, the approximation underestimates error. A practical guideline is to prefer the exact model whenever |mult·θ| approaches a few milliradians or when tolerance limits are tight.
Many benches specify an allowable radial error at a sensor, pinhole, or coupling lens. This tool computes r = √(x²+y²) and compares it to a user-defined tolerance radius. That simple pass/fail indicator helps standardize acceptance checks across operators and reduces subjective “looks aligned” judgments.
The correction outputs estimate the angular change required to drive x and y toward zero at the target plane. They are computed by inverting the propagation relationship through atan2. Apply corrections gradually, then re-measure. In practice, mechanical backlash and cross-coupling mean you should iterate, but the suggested values provide a strong first step.
Alignment work benefits from recorded inputs, outputs, and assumptions. Exporting CSV supports lab notebooks and QA logs, while print-to-PDF creates consistent reports for audits. If you calibrate your camera scale (mm per pixel), you can map measured spot shifts directly into x and y inputs, keeping the workflow quantitative and repeatable.
Use the measured translation of the beam or component at the reference plane. If you only measured at the target, set x0=y0=0 and represent the error using angles, or split based on your mechanical diagnosis.
Milliradians are often convenient for bench work because small tilts become simple numbers. Degrees are fine for larger adjustments. The calculator converts everything internally, so choose the unit that matches your measurement tool.
Set multiplier to 2 for a single steering mirror reflection. For multi-reflection paths, use an effective multiplier representing how much your measured actuator tilt changes the outgoing beam angle in the axis you care about.
Radial error is the combined displacement magnitude at the target plane: r = √(x²+y²). It is useful when your tolerance is circular, such as a detector active area, pinhole, or coupling acceptance window.
The approximate result assumes tan(a) ≈ a. That holds for very small a, but it increasingly underestimates the offset as angles grow. Use the exact value for tight tolerances or larger tilts.
They estimate the angular change needed to move the target-plane offset toward zero. Apply them as a starting point, then re-check. Real mounts can couple axes, so expect a few iterations for final alignment.
Yes. Convert pixel displacement to millimeters using your calibration, then enter x0/y0 or target offsets you back-calculate into angles. This makes alignment quantitative and improves repeatability across operators.
| L (m) | x0 (mm) | y0 (mm) | θx (mrad) | θy (mrad) | mult | x @ target (mm) | y @ target (mm) | r (mm) |
|---|---|---|---|---|---|---|---|---|
| 0.50 | 0.00 | 0.00 | 0.50 | 0.00 | 1 | 0.25 | 0.00 | 0.25 |
| 1.00 | 0.20 | -0.10 | 0.30 | -0.20 | 1 | 0.50 | -0.30 | 0.58 |
| 0.75 | -0.15 | 0.05 | 0.40 | 0.10 | 2 | 0.45 | 0.20 | 0.49 |
| 2.00 | 0.00 | 0.00 | 0.10 | 0.10 | 1 | 0.20 | 0.20 | 0.28 |
| 1.50 | 0.30 | 0.20 | -0.25 | 0.15 | 2 | -0.45 | 0.65 | 0.79 |
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.