Spectroscopy · 13 min
Focal length, grating, and slit are one decision wearing three names: how finely to spread the spectrum, and how much light you are willing to pay for it. Two relationships decide almost everything.
The governing trade-off
Every spectrograph specification sheet is these three relationships in different clothes. None is complicated alone; the difficulty is that resolution bought through any of them is paid for in photons.
Δλ/Δx ≈ 10⁶ · cos β / (m · G · f)
Focal length f and groove density G together set how many nanometres land on each millimetre of the focal plane. A 320 mm instrument with a 1200 g/mm grating delivers about 2.3 nm/mm; doubling either the focal length or the groove density roughly halves it.
FWHM ≈ dispersion × slit image
The spectrum is a stack of slit images, one per wavelength. At 2.3 nm/mm, a 100 µm slit means 0.23 nm of instrumental width stamped onto every feature — and the slit is the one resolution control you keep adjusting after the purchase.
throughput ∝ (1/f#)² → f/3.5 vs f/9.7 ≈ 7.7×
Longer instruments keep the same grating size, so the aperture slows as the focal length grows. The resolution of the 750 mm flagship costs nearly eight times the exposure of the 200 mm workhorse — resolution you do not need is integration time you pay forever.
resolution ≥ ~3 px × dispersion · coverage = dispersion × sensor width
An array detector samples the focal plane, and a peak needs roughly three pixels across its width to be measured rather than merely detected. With 26 µm pixels at 2.3 nm/mm that is a 0.18 nm floor no slit can beat — which is exactly the published CCD resolution of the 320 mm instrument, and why the same bench resolves 0.08 nm with a PMT behind an exit slit.
The same dispersion sets coverage: a 26.6 mm sensor at 2.3 nm/mm sees 61 nm per frame, a 13.3 mm sCMOS half that. Resolution and coverage are the same number spent two ways — the interactive below lets you watch them trade.
Interactive
The simulation puts two spectral lines through the real dispersion, aberration, and sampling numbers of the Omni-λ family. Close the slit and watch the noise rise before the peaks separate; swap the grating and watch coverage collapse as resolution arrives.
The dashed lines are where the two peaks really are. The solid trace is what the spectrograph records once focal length, grating, slit, and detector have had their say — and the noise floor is what the f/number charges for it.
wavelength (nm)
Dispersion
2.28 nm/mm
1200 g/mm, 320 mm
Bandpass
0.202 nm
≈ 6.7 cm⁻¹ at 550 nm
Coverage
61 nm
per detector frame
Throughput
1.00×
f/4.2 vs f/4.2, same slit
50 µm — the usual compromise
550 nm
0.60 nm — 19.8 cm⁻¹ at 550 nm
What limits you now
The detector and optics now dominate — closing the slit further mostly costs photons. Move to a longer focal length or a finer grating instead.
Dispersion is anchored to the published Omni-λ values (1200 g/mm at 435.8 nm) and extrapolated with the grating equation; the line width is a quadrature sum of slit image, per-model aberration blur, and detector sampling, which reproduces the published PMT and CCD resolutions to within roughly 20%. Grating blaze efficiency is not modelled — for that, use the turret planner. Use this to understand the shape of the trade-off, then confirm the numbers for your exact configuration with us.
At a glance
| Model | Focal length · aperture | Dispersion | Resolution | Relative light | Typically chosen for |
|---|---|---|---|---|---|
| Omni-λ200i | 200 mm · f/3.5 | 3.6 nm/mm | 0.28 nm CCD · 0.15 nm PMT | 1.44× | Laser-induced fluorescence, routine UV-Vis, throughput-limited work |
| Omni-λ300i | 320 mm · f/4.2 | 2.3 nm/mm | 0.174 nm CCD · 0.08 nm PMT | 1× (reference) | Raman, photoluminescence, general research spectroscopy |
| Omni-λ500i | 500 mm · f/6.5 | 1.7 nm/mm | 0.15 nm CCD · 0.046 nm PMT | 0.42× | Laser diode characterisation, closely spaced emission lines |
| Omni-λ750S | 750 mm · f/9.7 | 1.1 nm/mm | 0.09 nm CCD · 0.028 nm PMT | 0.19× | Atomic emission, plasma diagnostics, fine molecular structure |
| HiperS-320i | 320 mm · f/4.4 | 2.29 nm/mm | 0.12 nm CCD (15 µm px) · 0.06 nm PMT | 0.91× | Multi-track and multi-fibre spectroscopy, LIBS, low-light imaging |
Dispersion and resolution are the published values with a 1200 g/mm grating at 435.8 nm; CCD figures assume 26 µm pixels and a 10 µm slit. Relative light is (f/4.2 ÷ f/#)² against the Omni-λ300i.
The trade-offs above condense into defaults that most labs converge on independently. If your measurement is on this list, the instrument column is the one to price first.
| Measurement | First choice | Why |
|---|---|---|
| Routine UV-Vis scans, laser-induced fluorescence | Omni-λ200i | Bands are broad, so the f/3.5 aperture is worth far more than dispersion you would never use. |
| Raman and photoluminescence microscopy | Omni-λ300i | The industry-standard compromise: ~1–2 cm⁻¹ Raman resolution with an aperture that still keeps pixel dwell times sane. |
| Laser diode spectra, closely spaced emission lines | Omni-λ500i | Sub-0.05 nm PMT resolution separates longitudinal modes and doublets the 320 mm class merges. |
| Atomic emission, plasma diagnostics, calibration transfer | Omni-λ750S | Down to 0.028 nm — lines a few hundredths of a nanometre apart arrive as separate peaks, not a shoulder. |
| Multi-fibre inputs, multi-track detectors, LIBS | HiperS-320i | Toroidal mirrors remove astigmatism across the focal plane, so fibres stay on their own detector rows instead of bleeding into their neighbours. |
A defensible order
The order matters more than any single specification. Buying resolution first is the most common way to end up with an instrument that starves its own detector.
Write down the two closest features you need as distinct peaks, in nm at your working wavelength — converting from cm⁻¹ if you think in Raman shifts. That number, divided by the recorded image width, is the dispersion you need. Everything else in the decision serves this.
Coverage is dispersion times sensor width. If the full spectrum must land on the detector in one exposure — kinetics, LIBS, unstable sources — that caps how fine a grating you can run, or forces stitching. A scanning monochromator escapes the cap but pays per wavelength.
Pick the shortest focal length that meets step one, because photon collection falls as 1/f#². Between f/3.5 and f/9.7 lies a factor of nearly eight in light — resolution you do not need is exposure time you pay forever.
Groove density comes from step one, blaze from where your signal lives, and the remaining turret slots are cheap insurance for the experiments you have not designed yet. This is the one decision you can revisit after purchase — focal length is not.
The instruments
One Czerny-Turner bench at four focal lengths, plus an aberration-corrected variant. All share the 30 mm focal plane, motorised or manual slits from 10 µm, and interchangeable grating turrets — so the decision really is the focal length and what you hang on it.
The throughput pick. When bands are broad and signal is scarce, the fastest aperture in the family beats dispersion it would never use. Also the answer when the spectrograph must fit inside a larger instrument.
The default, and deservedly so: the focal length the Raman and photoluminescence world standardised on. A triple turret covers UV to NIR without opening the box, and the resolution floor is low enough for almost all molecular work.
The step you take when the 320 mm class merges lines you need separated — laser diode modes, crowded emission spectra — and you can afford the light lost to the slower aperture.
Flagship resolving power, to 0.028 nm with a PMT. For atomic lines, plasma diagnostics, and calibration work — bought for a known requirement, never as a general-purpose default.
The 320 mm class rebuilt with toroidal mirrors so the whole focal plane is in focus at once. If your input is a fibre bundle or your detector runs multiple tracks, this is not an upgrade — it is the requirement.
Every model is configured, not picked from a shelf: entrance and exit ports, slit drives, mirror coatings, and the grating turret all carry option codes. The builder walks the part number; the turret planner works out which gratings earn their slots.
The rest of the measurement
What arrives at the slit and what reads the focal plane decide whether the dispersion you paid for becomes data. These are the tools and companion guides for both ends.
Work out which groove densities and blaze wavelengths cover your range at your resolution before committing to a turret — the tool models the efficiency this guide deliberately leaves out.
Configure focal length, port layout, slits, coatings, and turret into an orderable part number.
Filter detectors by sensor, cooling, read noise, and pixel size against the coverage and sampling numbers from the lab above.
The companion guide on quantum efficiency and read noise — the other half of the detection budget.
If the spectrograph is for Raman, the excitation wavelength decides your Stokes range in nm — settle it first.
Order-sorting and laser-rejection filters. Second-order overlap is real: 400 nm light lands on top of 800 nm in first order unless something removes it.
The quiet failure mode of a well-specified spectrograph is the coupling in front of it. Light delivered faster than the instrument's f/number overfills the grating and comes back as stray light; light delivered slower underfills it and wastes resolution. Match the fibre NA or relay optics to the aperture ratio — it costs a lens and saves the specification you paid for.
Common questions
320 mm is the standard answer and the right default. A Raman band interval of 1 cm⁻¹ spans about 0.03 nm at 532 nm excitation and 0.06 nm at 785 nm, so a 320 mm instrument with an 1800 g/mm grating resolves the 1–2 cm⁻¹ that most solid-state and molecular work needs. Move to 500 or 750 mm only when you genuinely need to split lines below ~1 cm⁻¹ — and accept the throughput penalty knowingly.
Only until something else becomes the limit. Bandpass is dispersion multiplied by the recorded image width — slit image, aberration blur, and detector pixels combined. Once the slit is closed to the aberration floor and the detector samples at three pixels per resolution element, extra focal length still helps (it shrinks the nm value of every micrometre at the focal plane), but each step costs a slower f/number and light collection falls with its square.
Photon collection scales as 1/f#², so moving from the f/3.5 Omni-λ200i to the f/9.7 Omni-λ750S costs a factor of about 7.7 in collected light for the same source — the difference between a one-minute and an eight-minute acquisition. It also sets the coupling condition: light delivered faster than the spectrograph accepts overfills the grating and returns as stray light, so fibre NA or relay optics must be matched to the instrument, not just aimed at the slit.
Groove density sets dispersion and range: finer gratings spread the spectrum further (better resolution, less coverage per frame) and reach a shorter maximum wavelength in first order. Blaze wavelength sets where diffraction efficiency peaks, falling off on either side. Choose density from the resolution you computed, blaze from where your signal actually lives, and use a turret so one instrument can carry a survey grating and a high-resolution grating side by side.
Wide enough to pass the light you have, narrow enough that the slit image is not the dominant term in the instrument function. Below the aberration blur (~25–40 µm in this family) further closing buys almost no resolution and throws away signal linearly. With an array detector there is also little point closing far below about 2.5 pixels — the published 10 µm-slit specifications are measurement conditions, not recommended operating points.
The same optical bench in two roles. With an exit slit and a PMT it is a monochromator: one wavelength at a time, resolution set purely by slits and dispersion, ideal for scanning and calibration. With an array detector at the focal plane it is a spectrograph: a whole spectral window per frame. The Omni-λ family supports both port configurations simultaneously, so the honest answer is often one instrument used both ways.
Send us the two closest features you must separate and the light level you have. That is genuinely the whole input — the rest of the configuration follows from it, and we will work it through with you.