Measuring Optical Density Beyond the Stray-Light Floor

Why a spectrophotometer cannot verify an OD 6 filter, why the light source has to be spectrally cleaner than the filter under test, and a laser-and-detector procedure with an error budget that reaches OD 7: source clean-up, detector linearity by a calibrated attenuator chain, baffling, the stacked-filter floor test, and how to report the result.

Published September 12, 20267 min read

Scope

This article is a procedure for measuring the blocking depth of a deep filter, meaning an optical density of 5 to 7, where a spectrophotometer stops being able to tell the filter from itself. It covers why the standard instrument fails, what the light source must satisfy, a laser-and-detector method with its error budget, the stacked-filter test that reveals a floor, and what to write down. It applies to notch filters, laser-line and bandpass blocking, and dichroic rejection bands alike. For the definition and the dB conversion see the optical density entry; OD 6 is a transmission of $10^{-6}$ , or $-60$ dB.

Why the spectrophotometer stops at OD 3 to 4

A grating spectrophotometer measures transmission as the ratio of two detector readings, sample in and sample out. Its floor is stray light: the fraction of the lamp's power that reaches the detector at wavelengths other than the one the monochromator is set to, through grating scatter, higher diffraction orders, and reflections inside the instrument. That fraction is typically $10^{-3}$ to $10^{-5}$ for a single-grating instrument, the quantity ASTM E387 defines as the stray radiant power ratio, and it sets the deepest OD the instrument can report: with $10^{-4}$ of stray light, a perfect absorber reads OD 4. A filter that blocks OD 6 at 532 nm passes the stray light at every other wavelength unchanged, so the detector sees $10^{-4}$ and the instrument reports OD 4, an answer that is wrong by two orders of magnitude and looks perfectly plausible. Double-monochromator instruments reach $10^{-7}$ to $10^{-8}$ and can verify OD 6 with margin; they are uncommon, slow, and worth borrowing if one is nearby. Without one, the measurement moves to a laser.

The source must be cleaner than the filter

The same failure happens with a laser if the laser is not spectrally pure to better than the OD being measured. The filter blocks the line; everything else the laser emits goes straight through. A diode-pumped 532 nm laser with 30 dB of infrared suppression carries $10^{-3}$ of its power at 1064 nm, which the notch passes, so the measurement floors at OD 3 regardless of the filter. A diode laser with a side-mode suppression ratio of 45 dB has a broad amplified spontaneous emission pedestal whose integral outside a 17 nm notch is of order $10^{-4}$ to $10^{-5}$ of the line, which floors the measurement at OD 4 to 5. The cure is a clean-up filter on the source, a bandpass at the laser wavelength with blocking of OD 6 or better everywhere the notch transmits, and for a DPSS laser an infrared blocker as well. The cleaned source should be checked on an optical spectrum analyzer or, better, by the stacked-filter test below, because the OSA's own dynamic range is usually 60 to 70 dB and cannot certify a $10^{-7}$ pedestal. The point generalizes: any measurement of OD $N$ requires every other path from source to detector to be below $10^{-N}$ , and the source spectrum is one of those paths.

Procedure

The measurement is a ratio of two detector readings at least six decades apart, so the work is in making both readings trustworthy.

Clean the source. Place a bandpass clean-up filter (and an infrared blocker for a DPSS laser) directly after the laser. Set the beam to the diameter and collimation the filter will see in use; a convergent beam samples a range of angles, and the notch shifts with angle.
Baffle the path. Enclose the beam from laser to detector, put an aperture immediately before the detector, and confirm the dark reading with the beam blocked at the laser. With the laser on and the beam blocked just before the filter position, the reading must be below $10^{-7}$ of the unblocked signal; if it is not, scattered light is finding the detector around the filter and the enclosure needs work.
Establish detector linearity with an attenuator chain. A silicon photodiode is linear over more than six decades if it is never saturated, but the claim has to be demonstrated for the detector, gain setting, and beam in hand. Measure a neutral-density filter of nominal OD 3 by two readings (bare and with the ND) at a power where both are comfortably in range, at 10 mW and 10 µW for instance; that ND is now calibrated at this wavelength to the linearity of a 1000:1 ratio, which any photodiode and transimpedance stage meets. Repeat with a second ND 3. The two calibrated NDs are the bridge across the dynamic range.
Take the reference reading with both NDs in the beam and the filter under test out: 10 mW becomes 10 µW at the detector.
Take the sample reading with the filter under test in and both NDs out. For a 10 mW source and an OD 6 filter this is 10 nW, or 3 nA of photocurrent at 0.3 A/W, which is 300 times a typical 10 pA dark current and comfortable for a chopped, lock-in measurement or a well-shielded DC one. The OD of the filter is the OD of the two NDs plus the log ratio of the two readings, and the detector never saw more than three decades of ratio in any single comparison.
Run the stacked-filter test. Measure a second deep filter alone, then the two stacked. If the stacked OD equals the sum of the individual ODs, the measurement is above the floor; if the stack reads the same as the deeper single filter, a floor has been reached, and the number is the floor, not the filter.
Check the angle. Tilt the filter by the tolerance the application will use, 2° or 5°, and repeat; a notch that is OD 6 at normal incidence may be OD 4 at the edge of its cone-angle specification because the band has shifted onto the laser line.

Error budget

For a 10 mW source, an OD 6 filter, and the chain above, the terms that matter are these.

Term	Typical size	Effect at OD 6	Control
Source spectral impurity after clean-up	$10^{-7}$ to $10^{-8}$	Floor at OD 7 to 8	Bandpass plus IR blocker; stacked-filter test
Scattered light around the filter	$10^{-7}$ with baffles, $10^{-5}$ without	Floor at OD 7, or OD 5	Enclosure, aperture at detector, beam-blocked check
Detector dark and electronic noise	10 pA against 3 nA	0.3% of the reading	Chopper and lock-in, or shielding and averaging
ND calibration	1% per ND	0.004 in OD each	Calibrate each ND at the working wavelength and power
Detector nonlinearity across a 1000:1 step	0.5%	0.002 in OD	Keep every single ratio within three decades
Filter fluorescence under 10 mW	up to $10^{-7}$ of incident for colored glass, far less for hard coatings on fused silica	Floor at OD 7	Measure with a spectral filter before the detector if suspected
Laser power drift between readings	1%	0.004 in OD	Reference detector on a pick-off, or interleave readings

Summed in quadrature the calibration and drift terms give about 0.01 in OD, which is not the limit. The limit is whichever floor is highest, and the stacked-filter test is the only item in the table that measures the floor directly rather than estimating it. A reported OD 6.0 from a setup whose floor is OD 6.3 is a reported floor.

Out-of-band transmission and the edges

Depth is one number; the filter's usefulness depends on two others that this procedure does not give. The transmission outside the blocking band, which decides how much of the wanted light survives, is measured on a spectrophotometer, where 90% and 95% are easy to tell apart and stray light is irrelevant. The width of the deep region, which decides how close to the laser line a signal can be recovered, is measured with a tunable source or by stepping through the band with several laser lines, since the OD falls from 6 at the center to 2 or 3 at the edges of the quoted bandwidth, and a laser that drifts toward an edge is a laser that is no longer blocked. Both measurements belong beside the depth in the report.

Reporting

Record the laser wavelength and its measured linewidth or the clean-up filter used, the angle of incidence and beam convergence, the beam diameter and where on the filter it fell, the temperature, the detector and gain, the ND values and their calibration, the floor measured by the stacked-filter test, and the OD with its uncertainty. A statement of the form "OD 6.1 ± 0.05 at 532.0 nm, 0° ± 1°, 2 mm beam, floor OD 7.4" contains everything the next person needs, and a bare "OD 6" contains almost nothing.

References: ASTM E387, Standard Test Method for Estimating Stray Radiant Power Ratio of Dispersive Spectrophotometers by the Opaque Filter Method; H. A. Macleod, Thin-Film Optical Filters, 4th ed. (CRC Press, 2010), on the measurement of blocking; manufacturer application notes on measuring deep blocking in laser-line and notch filters (Semrock/IDEX, Chroma). The photocurrent, floor, and budget figures above are computed from the stated source power, responsivity, and attenuations.