Finding Spectral Illuminance from total Illuminance

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In summary: This equation takes into account the characteristics of the LED, the measured light, and the photometric and radiometric units. In summary, to find the spectral irradiance of a LED, you need to integrate the relative luminosity function and then divide it by the luminous efficacy function.
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sciencellama
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I'm trying to find the "Spectral" Illuminance (lux/nm) of a LED in order to find the spectral irradiance (watt/nm).

I am somewhat new to optics, especially when it comes to the radiometric and photometric units.

I understand that the Lux is just the watt/M^2 scaled to the human eye using the luminous efficacy for each wavelength.

I want to know if this method is correct.

What I have----
The relative luminosity function (call it L(λ)) lm-1

The total Illuminance from the source (~8 lux)

What I think I need to do----

Integrate my L(λ) function multiply by C and set that equal to 8
C is this "normalization" constant

(I based this off of the fact that if I have 3 lux of light A and 4 lux of light B on a surface, I will have 7 lux total. In this case A and B are different colours, and I have a full continuous spectrum of them ~350nm-600nm)

Then the spectral Illuminance call it S(λ)
is just C* L(λ)

now I can take this function, C* L(λ) and divide it by the luminous efficacy function η(λ)

finally my spectral irradiance function E(λ) is =C* L(λ) / η(λ)

Physically this equation incorporates the LED characteristics, the measured light, and the whole lumen/watt : photo/raido metric stuff.

Could someone tell me if this is correct and whether or not I missed something?

Thanks
 
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  • #2
! Yes, your method is correct. To calculate the spectral illuminance (lux/nm) of a LED, you need to integrate the relative luminosity function (L(λ)) over the desired wavelength range and then multiply it by a normalization constant C. Then, you can divide the result by the luminous efficacy function η(λ) to obtain the spectral irradiance (watt/nm).
 

1. What is spectral illuminance?

Spectral illuminance refers to the amount of light at different wavelengths that is received at a particular point in space, typically measured in lumens per square meter (lm/m²).

2. What is total illuminance?

Total illuminance, also known as illuminance or incident light, refers to the total amount of light falling on a surface, typically measured in lux (lx). It takes into account all wavelengths of light, regardless of their individual contributions.

3. How is spectral illuminance different from total illuminance?

Spectral illuminance and total illuminance are different ways of measuring light. While spectral illuminance measures light at specific wavelengths, total illuminance measures overall light intensity regardless of wavelength. They are often used together to understand the composition and distribution of light in a given space.

4. Why is it important to find spectral illuminance from total illuminance?

Knowing the spectral illuminance can provide more detailed information about the light in a given space, which can be useful for understanding the effects of different light sources and for designing lighting systems. It can also help identify potential issues with color rendering or uneven light distribution.

5. What factors can affect the relationship between spectral illuminance and total illuminance?

The relationship between spectral illuminance and total illuminance can be affected by factors such as the type of light source, the distance between the light source and the surface being measured, and any obstructions or reflections in the space. Additionally, the sensitivity of the measurement equipment and the spectral response of the human eye can also impact this relationship.

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