This online calculator evaluates optical properties of a filter — transmission T, absorption A and reflection R — across the visible band 380–780 nm. You can set filter thickness and material parameters, enter or auto-fill absorption α and surface reflection R, and pick a colour simulation to preview the perceived tint. The tool plots T(λ), A(λ) and R(λ), produces a compact data table and updates the colour swatch to reflect the calculated transmission.
The calculator automatically generates continuous spectra for transmission, absorption and reflection, presents tabulated values at convenient wavelengths and adjusts the preview block colour based on computed transmission. This accelerates material selection and quick feasibility checks for optics, photonics and colour design.
Table of Contents
Capabilities
- Specify filter thickness and tune absorption α and reflection R for standard and custom materials.
- Compute T, A and R at a user-selected wavelength and across the full visible range.
- Visualise spectra T(λ), A(λ) and R(λ) from 380 to 780 nm and export the chart as PNG.
- Preview the apparent colour of transmitted light by applying the calculated transmission to a colour swatch.
- Use the result for quick checks in imaging, illumination design and simple thin-film studies.
Core formulas
Transmission is modelled as:
$$
T = (1 – R)^2 \cdot e^{-\alpha \cdot d}
$$
where d is the thickness in millimetres.
Absorption is defined by energy conservation:
$$
A = 1 – T – R
$$
Reflection R is an input parameter representing Fresnel losses and any surface coatings; it may be wavelength-dependent in advanced models.
For dispersion-aware modelling use the Sellmeier relation:
$$
n^2(\lambda) = 1 + \sum_{i=1}^{3} \frac{B_i\,\lambda^2}{\lambda^2 – C_i}
$$
Here n is refractive index at wavelength λ (µm), and Bi, Ci are material constants from reference tables. From n(λ) you can calculate Fresnel reflection R(λ) at boundaries and refine T(λ) and A(λ), which is essential for narrowband and multilayer designs.
Worked example
Example input and quick result, numbers are illustrative:
- Material: glass; thickness 1.7 mm; set α = 0.130 1/mm; set R = 0.053.
- At λ = 540 nm the model yields transmission ≈ 64.2%, absorption ≈ 28.8% and reflection ≈ 5.3%.
- The generated spectrum (380–780 nm) shows higher transmission in the green-yellow band and stronger attenuation towards the blue end.
Sellmeier example
Sample Sellmeier coefficients (illustrative) for a common optical glass:
| Coefficient | Value |
|---|---|
| B1 | 1.05240123 |
| B2 | 0.245001110 |
| B3 | 1.01233055 |
| C1 (µm²) | 0.006120500 |
| C2 (µm²) | 0.021100200 |
| C3 (µm²) | 104.230000 |
Use published Sellmeier data for high-accuracy dispersion modelling. Calculated n(λ) feeds Fresnel equations and returns wavelength-dependent R(λ) and refined T(λ).
Material parameter ranges
| Material | α range (1/mm) | R range |
|---|---|---|
| Glass | 0.06–0.23 | 0.045–0.060 |
| Plastic | 0.11–0.33 | 0.035–0.065 |
| Film / gel | 0.21–0.54 | 0.025–0.035 |
| Metalised | 0.62–1.05 | 0.12–0.32 |
| Dichroic coating | 0.02–0.06 | 0.055–0.12 |
Filter types and spectral behaviour
| Filter | Typical effect | Approx. spectral region |
|---|---|---|
| Red | Passes long wavelengths, warms colour | 600–700 nm |
| Orange | Boosts mid-red contrast | 590–620 nm |
| Yellow | Removes blue/violet, increases clarity | 570–590 nm |
| Green | Transmits green band, useful for foliage contrast | 500–570 nm |
| Cyan | Blocks reds, passes blue–green | 490–520 nm |
| Blue | Reduces warm tones, cools image | 450–490 nm |
| Violet | Emphasises UV-leaning content | 400–450 nm |
| Magenta | Selective subtraction of green | combined bands |
| Neutral density | Uniform attenuation across spectrum | full visible |
| UV-cut | Blocks λ < 400 nm | <400 nm |
| IR-pass | Transmits λ > 700 nm | >700 nm |
| Bandpass | Passes a narrow band (±10–30 nm) | user-defined |
| Dichroic | Reflective at specific bands, transmissive elsewhere | scientific optics |
Neutral density filters
ND filters attenuate light uniformly across the visible spectrum and preserve colour balance. They are used to control exposure without shifting chromaticity and are important in measurement and imaging workflows. Example ND values:
| Type | Optical density (D) | Transmission | Stops |
|---|---|---|---|
| ND2 | 0.31 | 49% | 1 |
| ND4 | 0.62 | 24% | 2 |
| ND8 | 0.93 | 12% | 3 |
| ND16 | 1.25 | 6% | 4 |
| ND32 | 1.56 | 3% | 5 |
| ND64 | 1.88 | 1.6% | 6 |
| ND128 | 2.20 | 0.8% | 7 |
| ND256 | 2.52 | 0.4% | 8 |
Select material or choose custom mode and enter α and R. Set thickness and wavelength; the calculator returns T, A and R at the chosen λ and draws spectra for 380–780 nm. Inspect the table, export the chart, and use the preview to assess perceived tint.
Notes and limitations
- The simple exponential absorption model plus a fixed R is suitable for first-order estimates. Thin-film interference, multilayer stacks and angle-dependent behaviour require transfer-matrix or rigorous thin-film simulation.
- Sellmeier-based dispersion and Fresnel boundary calculations improve accuracy and should be used when precise spectral fidelity is required.
- Measurement and manufacturer data must be used for final design and production; this calculator is targeted at preliminary analysis and educational purposes.
Useful sources
- Hecht, E. — “Optics” — comprehensive textbook on light propagation and material optics.
- Born, M. & Wolf, E. — “Principles of Optics” — foundational reference for wave optics and thin-film theory.
- Filmetrics / Lambda / Thorlabs application notes — practical guides on thin films, coatings and spectral measurement.
- Refractive index database and Sellmeier tables (optical material repositories) — for material dispersion data.
David Parry — Senior Engineering Analyst
Specializing in electronics and physics-based simulations with 20+ years of engineering experience. David ensures the mathematical and physical accuracy of the tools at ProCalcLab.
