Signal-to-lux responseSignal x-axis; illuminance y-axis
Unit Converters
Illuminance Scale Calculator
Translate one live electrical or digital signal through declared calibration endpoints without silently clamping readings outside the calibrated span.
PHOTOMETER SIGNAL CALIBRATION
Map a live sensor signal to lux without hiding extrapolation
Use declared lower and upper calibration anchors to translate an electrical or digital signal into illuminance. The active point may move beyond the span; it is flagged rather than silently clamped.
Calibration boundary: endpoints must be distinct and their orientation is preserved. The page assumes a linear response; it does not correct sensor nonlinearity or saturation.
Mapped illuminance—
Position in span—
Calibration sensitivity—
Range state—
Signal span—
Illuminance span—
LIVE CALIBRATION CURVE
See anchors, active point, and extrapolation zones
The blue line is the declared linear mapping. Red-tinted outer zones sit beyond the signal endpoints; the live marker retains its mathematical value if it enters them.
| Element | Signal | Illuminance | Meaning |
|---|
HOW TO USE
Transcribe a calibration span exactly
- Enter the live output using the same signal unit as both anchors.
- Copy lower and upper signal endpoints from the sensor or transmitter calibration.
- Enter the lux value assigned to each endpoint without swapping orientation.
- Read mapped lux, fractional position, and sensitivity together.
- If extrapolated, review range, saturation, and the governing acquisition system before using the value.
SCALE FUNDAMENTALS
Six quantities define one affine map
CALCULATION METHOD
Resolve the fractional signal position, then map the output
f = (s−s0)/(s1−s0)E = E0 + f(E1−E0)k = (E1−E0)/(s1−s0)s uses the declared signal unit, E lux, f dimensionless, and k lux per signal unit.
ENDPOINT ORIENTATION
A descending sensor span is mathematically valid
The formula preserves endpoint direction. If increasing signal corresponds to decreasing lux, sensitivity is negative and the line descends. The calculator rejects equal endpoints because they create a zero denominator; it does not reorder them for convenience.
EXTRAPOLATION
A number outside the span is not proof of sensor capability
The line can be extended algebraically, but the detector, amplifier, transmitter, or logger may clip, saturate, or change slope. Use extrapolated output only for screening and retain the raw signal. Do not label it calibrated without supporting evidence.
PHOTOMETRIC RESPONSE
Electrical linearity does not establish photometric accuracy
A perfectly linear 4–20 mA output can still carry spectral mismatch, cosine-response error, zero drift, temperature dependence, or range uncertainty. Those effects belong to calibration and measurement evaluation, not the endpoint interpolation itself.
DETAILED CALCULATION PROCESS
Default 4–20 to 0–1000 lx mapping
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| s | Live signal | 12 | signal unit |
| s0,s1 | Signal anchors | 4, 20 | signal unit |
| E0,E1 | Lux anchors | 0, 1000 | lx |
- Signal span = 20−4 = 16.
- Lux span = 1000−0 = 1000 lx.
- Fraction = (12−4)/16 = 0.5.
- Mapped addition = 0.5 × 1000 = 500 lx.
- Mapped illuminance = 0 + 500 = 500 lx.
- Sensitivity = 1000/16 = 62.5 lx per signal unit.
- 0 ≤ 0.5 ≤ 1, so the point is interpolated.
- Reverse check: 4 + (500−0)/62.5 = 12.
RESULT INTERPRETATION
Fraction locates the point; sensitivity explains noise amplification
A fraction of zero or one is exactly on an endpoint. Values below zero or above one are extrapolated. High sensitivity means a small signal error becomes a larger lux error. Rounding occurs after mapping, so endpoint reconciliation stays exact.
EVIDENCE AND LINEAGE
Retain the complete calibration identity
Keep sensor model and serial, range, signal unit, wiring mode, supply, endpoint source, calibration date, spectral source, geometry, temperature, logger scaling, raw signal, timestamp, and any zero or dark correction performed upstream.
LIMITS AND EXCLUSIONS
What the line does not correct
- Nonlinearity between anchors.
- Saturation and clipping outside anchors.
- Spectral and cosine-response errors.
- Drift, hysteresis, temperature, and electrical noise.
- Calibration uncertainty and resolution.
WORKED DECISION CASES
Two active points, two actions
Midspan logger check
A 12-unit signal maps to 500 lx and lies inside the span. The technician can compare it with a direct meter while retaining endpoint evidence.
Overrange event
A 22-unit signal maps above 1000 lx mathematically, but the transmitter’s overrange behavior is undocumented. The page flags extrapolation and the value is not used as calibrated evidence.
TECHNICAL GLOSSARY
Calibration terms
- Anchor
- Declared signal-lux endpoint pair.
- Span
- Upper endpoint minus lower endpoint.
- Sensitivity
- Output change per signal change.
- Interpolation
- Mapping between anchors.
- Extrapolation
- Mapping beyond anchors.
- Saturation
- Failure to increase output with input.
- Dark offset
- Output when incident light is absent.
- Hysteresis
- Different response for rising and falling input.
IMPORTANT NOTE
Do not clamp an overrange signal to the nearest lux endpoint
Clamping hides the evidence that the acquisition chain left its calibrated interval. Preserve the raw signal and investigate range behavior.
Frequently asked questions
Must the signal be mA?
No. Use any consistent linear signal unit.
Can the scale descend?
Yes; endpoint orientation is preserved.
Why reject equal signal endpoints?
They create a zero span and undefined sensitivity.
Is extrapolation clamped?
No. It is calculated and explicitly flagged.
Does this correct nonlinearity?
No. It assumes a straight response.
Can lux anchors be equal?
No meaningful illuminance span would remain.
When should I recalibrate?
Follow the governing program and investigate drift or overrange evidence.
Why keep raw signal?
It allows later verification of scaling and acquisition behavior.
AUTHORITATIVE BASIS