Film optical density measurement with two-exposure HDR imaging

Developed film carries more contrast than one camera exposure can hold. A clear patch transmits essentially all the light; a dense patch can transmit under 0.1%; an 8-bit readout clips one end or drowns the other in noise. This guide sets out the two-exposure HDR method used in film densitometry: size the exposure pair from your own noise floor, flat-field correct against a clear-film reference, fuse the two frames, and read optical density that a calibrated step tablet can confirm.

Optical density and the range one exposure covers

Optical density compares the sensor signal with and without the film in place:

I0 is the light field with no film, I the light through the film, T the transmittance. A clear patch reads OD 0; OD 3 means the film passes one thousandth of the light.

A machine vision sensor is linear in exposure - signal is proportional to photons times time - so transmittance survives as a ratio of exposure-normalized gray values. The limit is the readout span. Take an 8-bit example: full scale is 255 DN and your dark frames show a noise floor near 3 DN, so the lowest trustworthy signal is about 4 times that, call it 12 DN. One exposure then spans 255/12 ≈ 21:1, which is log10(21) ≈ 1.3 decades of transmittance - OD 0 to about 1.3 in the best case, a little less once the calibration point sits under full scale. Densitometry routinely needs OD 3. One frame will not get there; two will.

What you need

• A mono area scan camera with manual exposure and gain and a linear response. The MV-CS200-10UM is a 20 MP mono USB3 camera with a 1" sensor and C-mount; rolling shutter is fine because the film holds still during each frame, and 20 MP leaves margin for the printed ID characters around a patch.
• A collimated backlight sized to one film patch, inside an enclosure that blocks room light.
• A constant-current driver for the panel.
• A calibrated step tablet with certified OD values per step.
• Dark frames at each exposure time: light off or lens capped.

A diffuse panel lights the film from many angles at once, so the reading mixes emulsion scatter into the density and drifts across the field. Densitometry therefore runs on collimated backlights: light crosses the film once, straight through. The LS-BKL-0830 gives a 120 x 120 mm collimated field at 24 V - one patch per shot.

Choose the exposure pair from three numbers

Measure these once, at the bench:

• FS, full scale: 255 DN at 8-bit readout.
• F, trusted floor: about 4 times the measured dark noise - 12 DN here.
• C, clear-film level at the short exposure: aim for 200-240 DN; the example uses 230 DN at 2 ms.

Each exposure covers log10(FS/F) ≈ 1.3 OD. A pair with ratio r pushes the top of the range up by log10(r):

For a film reaching OD 2.3, r = 10^2.3 × 12/230 ≈ 10. For OD 3.3, r ≈ 100.

Worked example with t1 = 2 ms and t2 = 20 ms:

• Short frame: clear film at 230 DN reads down to 12/230 = 5.2% transmittance, so it covers OD 0 to log10(230/12) = 1.28.
• Long frame: every signal is 10 times larger. Pixels stay unclipped while transmittance is at most 255/2300 = 11.1%, so the long frame covers log10(2300/255) = 0.95 to log10(2300/12) = 2.28.
• Merged: OD 0 to 2.28, with a 0.33 OD overlap band (0.95-1.28) where both frames work. That band is your seam check.

Both rows use the same inputs above. Scale t1 until clear film lands near 230 DN on your panel, then set t2 = r × t1.

Lock exposure and gain manually; any auto mode between frames destroys the ratio. To grab both frames on one trigger cycle from a single camera, follow Two exposure times one camera: alternate per trigger without serial. Fusion styles are compared in HDR imaging for surface inspection: capture and fusion; density work wants the deterministic one - keep the unsaturated pixel - because the number needs a known linear scale, not a blended look.

Capture, correct and fuse

1. Mount the film flat on the backlight, emulsion toward the camera, inside a light-tight enclosure. Ambient light adds signal to both film and flat, which compresses the ratio and reads as density too low.
2. At each exposure time, shoot 8-16 dark frames (light off) and 8-16 flat frames (film removed, carrier in place), and average each set.
3. Correct every image with the dark and flat shot at the same exposure time:

V is transmittance-referenced, and because dark and flat share the frame's exposure time, it is exposure-normalized too.

4. Fuse: take the short-exposure V at every pixel except those within about 1 DN of full scale, which take the long-exposure V. Both frames now share one reference, so the switch is invisible in the result.
5. Compute OD = -log10(V) per pixel. Keep 10- or 12-bit camera data through this step; rounding to 8-bit first quantizes the dense end before the log ever sees it.
6. Lay the step tablet where the film sits and run the same chain. Each certified step should land within about 0.02 OD of its printed value - the same gray-target discipline as camera dynamic range measurement with a gray step target, one step at a time.

Keep the light honest

OD is a ratio against the flat, so slow drift cancels - as long as the flat is fresh. LED panels brighten as they warm over the first 10-20 minutes and fade over months of run hours. Drive the panel with constant current: a constant-current light controller such as the LS-CTL-0180 - 4 channels, 120 W, for 24 V lights - holds output far steadier than an unregulated rail.

Track drift by watching the mean gray value of a fixed ROI on the flat across the day; the ROI and reference method is exactly that measurement. If the step tablet moves more than 0.02 OD between morning and afternoon, re-shoot the flat and find out what changed.

When the usual answer is wrong

• Film that stays within OD 0-2 on a 12-bit sensor: one exposure may cover it. Worked check: full scale 4095 DN, measured floor 30 DN gives 4095/30 ≈ 137:1, and log10(137) ≈ 2.1 OD. Confirm on the step tablet; past 2.1, go back to the pair.
• Colored or dyed film: OD changes with wavelength, so measure in the band the dose curve was fitted with. To escape room light, an infrared panel such as the LS-BKL-0416 moves the measurement to 850 nm; it runs constant-on only, so power it from a steady 24 V rail rather than strobing.

• Film that advances between the two frames: register the long frame to the short one before fusing, or take both exposures inside one trigger cycle as above.

Common mistakes

• Auto exposure or auto gain active between frames: the ratio r is gone, and OD steps at the seam.
• One dark or flat pair reused for both exposure times: dark signal scales with t, so the long frame comes out with wrong offsets.
• Rounding to 8-bit before fusion: the dense end is quantized before the log.
• Flat shot without the film carrier in place: holder shadows print into every reading.
• Step tablet skipped: linearity is then assumed, never shown.

Where to start

Size the panel first: the lights finder filters backlights by size, wavelength and type. The lighting step of the configurator pairs panel, driver and camera in one build, and the area scan cameras page narrows the camera choice. Related capture methods sit on the systems topic page, and /quote/ takes a parts list when the station is ready to price.