Calculate normalized intensity from sample, background, and reference light levels, or solve for any missing value in lux, fc, or cd/m².
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Normalized Intensity Formula
The normalized intensity compares a sample intensity to a background and reference intensity. The main formula is:
NI = (I_s - I_b)/(I_r - I_b)
The calculator can also rearrange the formula to solve for any missing value:
I_s = NI*(I_r - I_b) + I_b
I_b = (I_s - NI*I_r)/(1 - NI)
I_r = ((I_s - I_b)/NI) + I_b
- NI = normalized intensity, unitless
- I_s = intensity of sample
- I_b = intensity of background
- I_r = intensity of reference
To calculate normalized intensity, enter the sample, background, and reference intensities. To solve for one of the intensity values, enter normalized intensity plus the other two intensity values.
The intensity values are converted to a common base unit before calculation. The calculator uses lux as the base unit. Foot-candles are converted using 1 fc = 10.7639 lx. The cd/m² option is treated as numerically equal to lux for this calculator.
Intensity Unit Conversions and Normalized Result Ranges
| Unit | Symbol | Conversion used by calculator |
|---|---|---|
| Lux | lx | 1 lx = 1 lx |
| Foot-candle | fc | 1 fc = 10.7639 lx |
| Candela per square meter | cd/m² | 1 cd/m² = 1 lx for this calculation |
| Normalized intensity | Meaning |
|---|---|
| 0 | The sample equals the background intensity. |
| Between 0 and 1 | The sample is between the background and reference intensities. |
| 1 | The sample equals the reference intensity. |
| Less than 0 | The sample is below the background intensity. |
| Greater than 1 | The sample is above the reference intensity. |
Examples
Example 1: Calculate normalized intensity
You have a sample intensity of 70 lx, a background intensity of 20 lx, and a reference intensity of 120 lx.
NI = (70 - 20)/(120 - 20)
NI = 50/100 = 0.5
The normalized intensity is 0.5000.
Example 2: Calculate sample intensity
You have a normalized intensity of 0.75, a background intensity of 10 lx, and a reference intensity of 90 lx.
I_s = 0.75*(90 - 10) + 10
I_s = 0.75*80 + 10 = 70
The sample intensity is 70 lx.
FAQ
Can normalized intensity be greater than 1?
Yes. A normalized intensity greater than 1 means the sample intensity is higher than the reference intensity, assuming the reference is greater than the background.
Can normalized intensity be negative?
Yes. A negative value means the sample intensity is lower than the background intensity, assuming the reference is greater than the background.
Why can the reference and background not be the same?
The formula divides by the difference between the reference and background intensities. If they are the same, the denominator is zero, so normalized intensity cannot be calculated.