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LightCalc — The Science

This page explains exactly how LightCalc's two calculation models work, where they come from, and where they break down. If you've been gaffing for 20 years and trust your light meter more than any app, good — you should. Read this first.

Contents

  1. Units: fc, lux, lux@1m
  2. Inverse Square Law
  3. Model A — Gaffer Approximation
  4. Model B — Area Source (Physics)
  5. Diffuser Transmission
  6. Beam Angle & Coverage
  7. Diffuser Directionality (BTDF)
  8. 2-Stage Light Chain
  9. Exposure Guide: fc → T-stop
  10. Gaffer Rules of Thumb
  11. Known Limitations
  12. References

1. Units: fc, lux, lux@1m

Footcandles (fc) — the illuminance on a surface, measured in lumens per square foot. One footcandle = one lumen falling on one square foot. The unit film and TV production uses because it maps directly to exposure.

Lux (lx) — the SI equivalent: lumens per square meter. One footcandle = 10.764 lux. LightCalc works internally in lux and converts to fc for display.

Lux @ 1m — manufacturer-published center-beam illuminance at 1 metre from the fixture, full power, open face, no modifier. This is the baseline spec LightCalc uses. It's always a center-beam measurement — the edges of the beam are dimmer.

⚠️ Important
Lux@1m specs vary by manufacturer test conditions. Some test in a dark room with a calibrated sensor; others are less rigorous. Treat them as good approximations, not gospel. Your incident light meter at the subject is always ground truth.

2. Inverse Square Law

Light from a point source spreads in all directions. As it travels, it covers an increasing sphere of surface area. The surface area of a sphere is 4πr² — so at twice the distance, the same light covers 4× the area, meaning the intensity at any point is ¼ what it was.

E₂ = E₁ × (d₁² / d₂²) Or equivalently: E = I / d²
E = illuminance (lux), I = intensity (candela), d = distance (metres)

So if a fixture measures 10,000 lux at 1m, at 3m it's 10,000 / 9 = 1,111 lux. At 5m: 10,000 / 25 = 400 lux.

🎬 Gaffer Rule of Thumb
Double the distance = 2 stops less light. Half the distance = 2 stops more. Move a lamp from 10ft to 14ft (√2 × 10) = 1 stop loss. This works precisely for point sources. For large soft sources, falloff is shallower — see Model B.

The ASC published a thorough field test confirming this ("Revisiting — and Updating — Inverse-Square Law," American Cinematographer), which also demonstrated that soft source falloff is measurably shallower than point source falloff — which is why LightCalc has two models.

3. Model A — Gaffer Approximation

The "Practical estimate" model treats the entire rig — fixtures, diffuser, all — as a single modified point source. It's what a gaffer does mentally on set.

E_talent = (lux₁ₘ × qty × T_diffuser) / d_total_m² fc = E_talent / 10.764
d_total = fixture-to-diffuser distance + diffuser-to-talent distance, in metres
T_diffuser = diffuser transmission (0–1)

This collapses the whole rig into one distance and one efficiency multiplier. It's fast, intuitive, and reasonably accurate when:

It breaks down when the diffuser is large relative to the subject distance — e.g., a 12×12 frame with the talent 4ft underneath it. In that case, the diffuser cannot be approximated as a point source.

🎬 Gaffer Rule of Thumb
"The point source rule stops working when you're closer to the source than its longest dimension." A 12×12 diffuser: point source approximation breaks down inside ~12 feet. Model B takes over from there.

4. Model B — Area Source (Physics)

When the diffuser is large relative to the subject distance, it must be modeled as an extended area emitter, not a point source. This is the standard approach in physically-based rendering (Unreal Engine, Arnold, V-Ray all use this).

Step 1: Illuminance on the diffuser face

E_diffuser = (lux₁ₘ × qty) / d_FD_m²
d_FD = fixture-to-diffuser distance in metres

Step 2: Diffuser luminous exitance

M = E_diffuser × T_diffuser (lm/m²)

Step 3: Diffuser luminance (Lambertian assumption)

A Lambertian surface emits light equally in all forward directions, with intensity proportional to the cosine of the angle from the surface normal (Lambert's cosine law, 1760). This is the standard model for diffusion materials.

L = M / π (cd/m²)
L = luminance of the diffuser face. The π comes from integrating the Lambertian emission over the hemisphere.

Step 4: Illuminance at the talent — projected solid angle

The illuminance at a point from a Lambertian area source equals the luminance multiplied by the projected solid angle of the source as seen from that point:

E_talent = L × Ω_proj

For a rectangular source, the projected solid angle has a closed-form analytic solution (derived from Fock, 1924; used in radiosity rendering since the 1980s). For a point on the centre normal of a rectangle with half-widths a and b at perpendicular distance d:

Let X = a/d, Y = b/d Ω_proj = 2 × [ X/√(1+X²) × arctan(Y/√(1+X²)) + Y/√(1+Y²) × arctan(X/√(1+Y²)) ]
This is exact — no approximation. Implemented directly in LightCalc's Mode B calculation.

For off-axis points (secondary point / background), the rectangle is split into up to four sub-rectangles about the perpendicular foot of the measurement point, and the formula is applied to each quadrant and summed or subtracted as appropriate.

📐 Why this matters
At close distances to a large diffuser, the solid angle is nearly π steradians (the full hemisphere) — meaning the talent is bathed from nearly every forward direction. Falloff from a large near source is dramatically shallower than inverse square. This is why a 12×12 overhead gives flatter coverage than a point source would — and why Model A over-predicts falloff in this regime.
🎬 Gaffer Rule of Thumb
"Big source close up = flat falloff." A 12×12 at 8ft overhead lights a 10ft-wide area very evenly. Move the talent 4ft to one side: maybe half a stop difference. A point source at the same apparent height? Two stops difference across the same move. This is the area source effect — and it's real, measurable, and what Model B captures.

5. Diffuser Transmission

LightCalc models diffusion as a simple transmission multiplier T applied to the luminous exitance. Real diffusion materials have a BTDF (bidirectional transmittance distribution function) — they're not perfectly Lambertian — but this is a good first approximation for most materials.

DiffuserTransmission (T)Stop LossNotes
Open Face1.000No diffuser
¼ Grid0.85~0.23Minimal scatter, mostly forward
½ Grid0.501.0Most common key light diffuser
Full Grid0.252.0Heavy diffusion, even scatter
Light Grid0.35~1.5Between ½ and full
Opal0.30~1.75Very even scatter, near-Lambertian
⚠️ These are practical approximations
Actual transmission varies by manufacturer, age, and how the material is tensioned. Rosco, Lee, and other manufacturers publish measured transmission data for their materials. Measure your own with a meter if precision matters.

6. Beam Angle & Coverage

The lux@1m spec is always measured at the center of the beam. At the edge of the beam angle (defined as the angle where intensity drops to 50% of center), you're already 1 stop down.

LightCalc uses beam angle to calculate what fraction of the diffuser panel is actually illuminated by the fixture:

beam_radius_at_diffuser = d_FD × tan(beam_angle / 2) beam_area = π × beam_radius² coverage = min(1.0, diffuser_area / beam_area)
If beam is wider than the diffuser: coverage = 1.0 (fully illuminated, but some output is wasted past the edges)
If beam is narrower: only the illuminated fraction contributes to the area source
🎬 Gaffer Rule of Thumb
"You need your beam to cover the frame." Three LS600x in a row at 4ft from a 12×12: each fixture has a ~120° beam angle → 4 × tan(60°) = 6.9ft radius. Fine for coverage. Put them on Fresnels at 15° spot: 4 × tan(7.5°) = 0.5ft radius. You're hot-spotting the center. The calculator shows this as a coverage percentage.

7. Diffuser Directionality (BTDF)

Real diffusion materials are not perfectly Lambertian. A ¼ grid passes most light nearly straight through (forward-biased). Full opal scatters almost uniformly in all forward directions (near-Lambertian). This affects how the diffuser behaves as an area source.

LightCalc's BTDF slider (0–100%) interpolates linearly between two extremes:

E_final = E_lambertian × (1 − scatter) + E_pointsource × scatter
scatter = BTDF slider value (0.0 to 1.0)

Default values per material: Opal 10% (near-Lambertian), Full Grid 20%, ½ Grid 50%, ¼ Grid 75%, Open Face 100%.

8. 2-Stage Light Chain

When a modifier is on the fixture (Fresnel, softbox, umbrella, beauty dish), LightCalc models a two-stage chain:

[Fixtures] → [Modifier 1] → [Distance 1] → [Main Diffuser] → [Distance 2] → [Talent]

Point source modifiers (Fresnel, Par)

These narrow and redirect the beam. The output is still a point source, with a modified beam angle and an efficiency multiplier applied.

lux_out = (lux₁ₘ × qty × η_modifier) / d1_m² beam_angle_eff = modifier_beam_angle (overrides fixture setting)
η_modifier = modifier efficiency (Fresnel flood: 0.80, spot: 0.70, etc.)

Area source modifiers (Softbox, Umbrella, Beauty Dish)

These create a new area emitter at the fixture position. The calc becomes area source → area source — two applications of the projected solid angle formula in series.

Step 1: L_modifier = (lux₁ₘ × qty × η_modifier) / π (luminance of modifier face) Step 2: E_diffuser = L_modifier × Ω_proj(modifier → diffuser) (illuminance at diffuser) Step 3: Run standard Mode B from E_diffuser through diffuser → talent
Ω_proj is the projected solid angle of the modifier face as seen from the diffuser center.
For a circular modifier (umbrella, beauty dish), approximate as a square with same area.
🎬 Gaffer Rule of Thumb
"Every modifier costs you light." Fresnel attachment: ~0.5 stop. Softbox: ~0.75 stop. Silver umbrella: ~0.3 stop. White umbrella: ~0.7 stop. Beauty dish: ~0.5 stop. Stack a modifier on a fixture before shooting through a diffusion frame and you're giving up 1–1.5 stops before you even start.

9. Exposure Guide: fc → T-stop

The relationship between illuminance and exposure follows the standard photometric exposure equation:

N² / t = (E × S) / (C × K)
N = f-number, t = shutter time, E = illuminance (lux), S = ISO, C = lens transmission factor, K = reflected light meter calibration constant (typically 12.5)

LightCalc uses a simplified practical version calibrated to incident light (not reflected):

fc_required = (T² × fps) / (ISO / 800) EV₁₀₀ = log₂(fc × 10.764 / 2.5)
fps assumed = 24 (1/48 shutter at 180°). EV₁₀₀ is the standard photographic exposure value at ISO 100.
T-stopfc needed (ISO 800, 24fps)fc needed (ISO 3200)
T2~16 fc~4 fc
T2.8~32 fc~8 fc
T4~64 fc~16 fc
T5.6~128 fc~32 fc
T8~256 fc~64 fc
T11~512 fc~128 fc
⚠️ These are guidelines, not guarantees
Actual exposure depends on shutter angle, frame rate, ND in the camera, lens transmission (T-stop vs f-stop), and the specific camera/sensor response. Always use your incident meter at the subject to confirm.

10. Gaffer Rules of Thumb (collected)

Double distance = 2 stops down
Exact for point sources. For soft sources, more like 1–1.5 stops over the same distance ratio.
Point source rule breaks down at the source diagonal
A 12×12 diffuser: treat as a point source only when the subject is more than ~12ft away. Inside that, use area source math.
Big source close up = flat falloff
Large overhead diffuser at close range: talent can move 5ft and barely register on the meter. Same fixture as a point source: 1–2 stop swing across the same move.
Every modifier costs you light
Fresnel: ~0.5 stop. Softbox: ~0.75 stop. White umbrella: ~0.7 stop. Silver umbrella: ~0.3 stop. Beauty dish: ~0.5 stop. ½ grid: 1 stop. Full grid: 2 stops. Opal: ~1.75 stops.
Your beam needs to cover the frame
If your beam angle at distance doesn't fully cover the diffusion frame, you're hot-spotting — the area source calc is wrong because only part of the diffuser is lit. Move the fixture back, or spread the beam.
Background: √(height² + distance²)
Distance from your overhead diffuser to a background point 15ft away at talent height is √(8² + 15²) = 17ft. Then apply cos(angle) for the oblique hit. Expect 3–4 stops below talent for a typical overhead rig.
The meter is always right
All of this math assumes perfect geometry, perfect fixtures, and idealized diffusion materials. On set: measure at the subject. Use the calculator to plan and predict, use the meter to confirm.

11. Known Limitations

LimitationImpactWorkaround
Uniform diffuser illumination assumed One fixture creates a hotspot on the diffuser, not uniform luminance. Model B over-estimates evenness. Use multiple fixtures spread across the frame, or increase fixture-to-diffuser distance.
Multiple fixtures treated as one point source Three LS600x in a row have different beam overlap at different positions on the diffuser. Conservative estimate: assume the center of the diffuser is the best-lit point.
Diffusers are not perfectly Lambertian Grid cloth transmits more on-axis than off-axis. Use the BTDF slider to compensate. Measure your specific material if precision matters.
No bounce or ambient modeling On-set bounce from white walls, ceilings, and reflectors adds fill. Calculator shows direct only. Add 0.3–1 stop fill for practical on-set environments.
Lux@1m specs vary by test conditions Some manufacturers are optimistic. Real output may be 10–20% lower. Load the IES file from the manufacturer for more accurate beam data.
No spectral modeling Transmission values are broadband. Blue gels transmit much less than white light averages suggest. Measure gel-filtered output with your meter when using heavy color.

12. References

LightCalc is a planning tool. Results are estimates based on idealized models and manufacturer specifications. Always confirm exposure with an incident light meter at the subject position. Built by Smith Creative Technologies.