Monochromator Bandwidth Calculator

Formula Used

A monochromator maps wavelength into position at the slit plane. With reciprocal linear dispersion D_r (nm/mm), the spectral bandwidth is:

Two practical models for effective slit width:

• Simple: w_eff = w_out
• Entrance+Exit (RSS): w_eff = √[(M·w_in)² + w_out²]

Common derived quantities:

• Resolving power: R = λ / Δλ
• Wavenumber bandwidth: Δσ ≈ (10⁷ / λ²)·Δλ (cm⁻¹), using λ and Δλ in nm
• Frequency bandwidth: Δν ≈ (c/λ²)·Δλ, with λ and Δλ in meters

How to Use This Calculator

1. Enter the central wavelength for your scan region.
2. Provide reciprocal linear dispersion at that wavelength.
3. Enter entrance and exit slit widths using µm or mm.
4. Choose the model that matches your optical layout.
5. Press Calculate to view bandwidth above the form.
6. Use Download CSV or Download PDF for records.
7. If needed, set a target Δλ and solve the exit slit.

Tip: Start with the RSS model for realistic results, then compare the simple estimate to understand which slit is dominating the bandpass.

Example Data Table

Representative settings for a visible-light grating monochromator. Values are illustrative; use instrument documentation for your dispersion.

Monochromator Bandwidth Guide

1) What the bandwidth number really means

A monochromator does not output a single wavelength; it outputs a narrow band whose width is the spectral bandwidth Δλ. In typical laboratory scans, Δλ sets the smallest feature you can resolve. For example, a 0.10 nm bandpass can distinguish closely spaced lines better than a 0.50 nm bandpass, but it will transmit less optical power.

2) Reciprocal linear dispersion as the core scaling

Reciprocal linear dispersion D_r (nm/mm) links position at the slit plane to wavelength. Lower D_r means more wavelength change per millimeter of slit width, producing a narrower Δλ for the same slit. Many grating instruments fall in the ~0.5–5 nm/mm range depending on focal length, groove density, and grating angle, so entering the correct value matters.

3) Why entrance and exit slits both contribute

The exit slit selects part of the dispersed spectrum, while the entrance slit defines the width of the image projected onto the exit plane. When the entrance image is comparable to the exit slit, the combined bandpass broadens. The RSS model used here approximates that combination as w_eff=√[(M·w_in)²+w_out²], which is a practical estimate for many scanning monochromators.

4) Throughput–resolution tradeoffs you can quantify

Slit width changes bandwidth almost linearly through Δλ=D_r·w_eff. If D_r=1.2 nm/mm, increasing w_eff from 0.05 mm to 0.10 mm increases Δλ from 0.06 nm to 0.12 nm. That same change can significantly raise detector signal, which is valuable when source brightness is limited or when fast scanning is required.

5) Converting to wavenumber and frequency bandwidth

Spectroscopy often reports bandwidth in cm⁻¹. Near 532 nm, a 0.10 nm bandwidth corresponds to about 3.5 cm⁻¹ using Δσ≈(10⁷/λ²)·Δλ with λ in nm. The calculator also reports Δν in THz, useful when comparing to laser linewidths, modulation bandwidths, or detector response times.

6) Real-world broadening beyond slit geometry

Even with narrow slits, the practical bandpass can widen due to aberrations, finite grating imaging quality, stray light, and detector aperture. A common practice is to measure the instrument function using a narrow spectral line source and treat the computed Δλ as a baseline. If measured line widths exceed the prediction, optical alignment and scatter control are likely limiting factors.

7) Using a target Δλ to set the exit slit

When you know the required bandpass (for example, matching a filter bandwidth or a spectroscopic linewidth), use the target option to solve for the exit slit. In the RSS model, the calculation checks whether the target is physically achievable given the entrance slit and magnification. If the target is too narrow, reducing the entrance slit or magnification is the correct next step.

8) Documenting settings for repeatable measurements

Bandwidth depends on several settings that can drift between sessions. Recording λ, D_r, w_in, w_out, and model choice makes results reproducible across operators and instruments. The CSV export provides a quick lab log, while the print-to-PDF option preserves a formatted record for reports, calibration notes, and method validation.

FAQs

1) What is a typical slit width range?

Many instruments use 10–2000 µm. Narrow slits improve resolution but reduce signal. Start around 50–200 µm, then adjust based on required Δλ and detector noise.

2) Which model should I choose?

Use the RSS model for most setups because it accounts for both slits and imaging. Use the simple model only for quick estimates when the entrance slit image is much smaller than the exit slit.

3) Where do I find reciprocal linear dispersion?

It is usually in the instrument manual or calibration sheet, sometimes as nm/mm versus wavelength. If unavailable, measure a known spectral line separation on the focal plane and compute nm per mm.

4) Why does Δλ change when I change wavelength?

D_r is wavelength dependent because grating angles and imaging conditions change across the scan. Update D_r for the wavelength region you care about for best accuracy.

5) What does resolving power represent?

Resolving power R=λ/Δλ describes how finely the monochromator can separate wavelengths. Larger R means finer discrimination. It is a convenient single-number summary when comparing configurations at the same λ.

6) Why does the target solve sometimes return no solution?

If the entrance slit image alone already exceeds the required effective width, the desired Δλ is not achievable without changing optics. Reduce w_in, reduce magnification, or use a higher-dispersion configuration.

7) Is this bandwidth the same as the spectral step size in a scan?

No. Step size is how far you move between measurement points. For clean spectra, choose a step size smaller than Δλ, often Δλ/2 to Δλ/5, to avoid undersampling features.