# Calculate Retinal irradiance - from photometric units

• I
• az32
In summary: However, based on the information provided, it seems that you are trying to determine the retinal irradiance value for a 1 blue LED system. To do this, you approximated the LED as monochromatic using the 460 nm peak and used the scotopic eye sensitivity curve to convert the lumen value to radiant power. After this, you used ray tracing software to determine the percentage of the LED that reaches the pupil and calculated the irradiance by dividing the radiant power by the illuminated retinal area. However, you then mention the need for the value in log photons/cm2/s, which would require converting W into photons/s. It is not clear which curve (scot
az32
I have been trying to calculate what retinal irradiance value I get with a 1 blue LED system.

Since the manufacturer didn´t give the spectral distribution information, I will approximate LED as a monochromatic one (using the 460 nm peak).

From the datasheet, the LED intensity range goes from 6 lumen to 30 lumen. For the 6 lumen case, I used scotopic eye sensitivity curve (i want to apply the stimulus in a dark room) to convert the lumen value to radiant power (W). I simply divided the 6 lumens per the sensitivity times the 1700 normalization coefficient. Is this process right? I reached a value of 0.006W.

I know from the ray tracing software that only 3.7º of the LED (total from the center) reach the pupil. So, from the spatial LED curve, the 0.006W become approximately 1.57×10−4W (i traced a trapezium over the graphic and divided the areas)

The illuminated retinal area is 0.0031cm2

So I calculated the irradiance dividing the 1.57×10−4W by the area of 0.0031cm2, having a value of 0.05W/cm2
However, I need this value in log photons/cm2/s

Can you validate my logic? Thanks!

az32 said:
I have been trying to calculate what retinal irradiance value I get with a 1 blue LED system.

Since the manufacturer didn´t give the spectral distribution information, I will approximate LED as a monochromatic one (using the 460 nm peak).

From the datasheet, the LED intensity range goes from 6 lumen to 30 lumen. For the 6 lumen case, I used scotopic eye sensitivity curve (i want to apply the stimulus in a dark room) to convert the lumen value to radiant power (W). I simply divided the 6 lumens per the sensitivity times the 1700 normalization coefficient. Is this process right? I reached a value of 0.006W.

I know from the ray tracing software that only 3.7º of the LED (total from the center) reach the pupil. So, from the spatial LED curve, the 0.006W become approximately 1.57×10−4W (i traced a trapezium over the graphic and divided the areas)

The illuminated retinal area is 0.0031cm2

So I calculated the irradiance dividing the 1.57×10−4W by the area of 0.0031cm2, having a value of 0.05W/cm2
However, I need this value in log photons/cm2/s

Can you validate my logic? Thanks!
What eyes are you using? Edit as in radiometer? Cells ?

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az32 said:
From the datasheet, the LED intensity range goes from 6 lumen to 30 lumen. For the 6 lumen case, I used scotopic eye sensitivity curve (i want to apply the stimulus in a dark room) to convert the lumen value to radiant power (W). I simply divided the 6 lumens per the sensitivity times the 1700 normalization coefficient. Is this process right? I reached a value of 0.006W.

You are on the right track (lumens does convert to Watts), but I have the luminous efficacy (visibility factor) at 460 nm as 0.06, giving an eye response value of 683 lm/W * 0.06 = 41 lm/W, so I calculate a range of 0.146 W (6 lm) to 0.73 W (30 lm). As usual, I refer to Wolfe's 'Introduction to Radiometry'.

az32 said:
I know from the ray tracing software that only 3.7º of the LED (total from the center) reach the pupil. So, from the spatial LED curve, the 0.006W become approximately 1.57×10−4W (i traced a trapezium over the graphic and divided the areas)

I'm not entirely sure what you are doing here, but you seem to have the general idea correct.

az32 said:
However, I need this value in log photons/cm2/s

Ruh roh... now you need to convert W into photons/s. I guess you could go with something like Watts = number of photons/s * hc/λ.

Andy Resnick said:
You are on the right track (lumens does convert to Watts), but I have the luminous efficacy (visibility factor) at 460 nm as 0.06, giving an eye response value of 683 lm/W * 0.06 = 41 lm/W, so I calculate a range of 0.146 W (6 lm) to 0.73 W (30 lm). As usual, I refer to Wolfe's 'Introduction to Radiometry'.
I'm not entirely sure what you are doing here, but you seem to have the general idea correct.
Ruh roh... now you need to convert W into photons/s. I guess you could go with something like Watts = number of photons/s * hc/λ.

Thank you for your answer.

I am planning to apply the stimulus to human dark adapted eyes.
So, I should not use the scotopic curve instead of the photopic?
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/bright.html#c4
In the scotopic curve, the efficacy conversion factor is 1700 lm/W. At 460 nm, the visibility factor is 0.567, giving an eye response value of 1700*0.567 = 963.9 lm/W.
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/efficacy.html#c1This represents a huge difference comparing with the photopic curve, and I'm not sure which curve I should use.

I agree with your suggestion to convert W into photons/s, thanks!

pinball1970 said:
What eyes are you using? Edit as in radiometer? Cells ?

Thank you for answer.
I'm planning to apply blue stimulus to the human eyes.

What do you mean with 'Edit as in radiometer?' ?

Thanks!

az32 said:
Thank you for your answer.

I am planning to apply the stimulus to human dark adapted eyes.
So, I should not use the scotopic curve instead of the photopic?
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/bright.html#c4
In the scotopic curve, the efficacy conversion factor is 1700 lm/W. At 460 nm, the visibility factor is 0.567, giving an eye response value of 1700*0.567 = 963.9 lm/W.
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/efficacy.html#c1This represents a huge difference comparing with the photopic curve, and I'm not sure which curve I should use.

I agree with your suggestion to convert W into photons/s, thanks!

Got it- you are right. Sounds like you should use the scotopic curve.

Edit: Wait, hang on. If the LED manufacturer is providing a spec in lumens, it means that someone already converted the radiometric output to photometric units; the manufacturer (or whomever is providing the 6-30 lm spec) already chose either the scotopic or photopic curve. If you can start out with the actual Watt output of the LED, you can choose whichever normalization curve you want.

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Andy Resnick said:
Got it- you are right. Sounds like you should use the scotopic curve.

Edit: Wait, hang on. If the LED manufacturer is providing a spec in lumens, it means that someone already converted the radiometric output to photometric units; the manufacturer (or whomever is providing the 6-30 lm spec) already chose either the scotopic or photopic curve. If you can start out with the actual Watt output of the LED, you can choose whichever normalization curve you want.

Thank you for your answer.
The manufacturer datasheet does not provide the actual watt ouput of the LED..only the intensity in lumens

In the manufacturer website there are some informations about the LED characteristics:

The Watt values they refer, are related to the consumed power, not the radiant...

I'm really struggling with this problem.

az32 said:
Thank you for answer.
I'm planning to apply blue stimulus to the human eyes.

What do you mean with 'Edit as in radiometer?' ?

Thanks!
Sorry that should have been Edit: As in radiometer. You can measure CCT SPD and lux then calculate the lm factoring in the viewing area. That is what I do but that is bucket physics compared to the really accurate Science you are probably looking at.

How are you using human eyes used to assess?

Are these eyes in alive people? Sorry I am not being facaeious I am interested from a biological and physics point of view.

@sophiecentaur @Andy Resnick @berkeman and @phinds can you confirm the maths.

One last thing, there is an issue with LED blue light and possible retinal damage.

A few studies in from France dept of Health one in Spain there will be others.
A consideration for your study group perhaps.

berkeman
az32 said:
I'm planning to apply blue stimulus to the human eyes.
pinball1970 said:
Are these eyes in alive people? Sorry I am not being facaeious I am interested from a biological and physics point of view.
I was concerned about that also. @az32 -- What exactly is this project? If this is at school or work, what oversight do you have from a supervisor and safety officer? What research have you done into safe illumination levels for the human eye (especially over wavelength ranges)? Is this for a product design? If so, what standards are you following for safe exposure for the human eye?

pinball1970
pinball1970 said:
Sorry that should have been Edit: As in radiometer. You can measure CCT SPD and lux then calculate the lm factoring in the viewing area. That is what I do but that is bucket physics compared to the really accurate Science you are probably looking at.

How are you using human eyes used to assess?

Are these eyes in alive people? Sorry I am not being facaeious I am interested from a biological and physics point of view.

@sophiecentaur @Andy Resnick @berkeman and @phinds can you confirm the maths.

One last thing, there is an issue with LED blue light and possible retinal damage.

A few studies in from France dept of Health one in Spain there will be others.
A consideration for your study group perhaps.

berkeman said:
I was concerned about that also. @az32 -- What exactly is this project? If this is at school or work, what oversight do you have from a supervisor and safety officer? What research have you done into safe illumination levels for the human eye (especially over wavelength ranges)? Is this for a product design? If so, what standards are you following for safe exposure for the human eye?

Hi. Thank you for your answers.
Yes, the main goal is to apply to alive people and I'm aware of the exposure standars for the different wavelengths. For example: https://www.researchgate.net/publication/326358672_Blue_Light_Hazard_Are_exposure_limit_values_protective_enough_for_newborn_infants

No in vivo testing will be performed until all is properly measured and tested under experimental conditions.
I'm just in a preliminary phase and, in order to choose a LED, I need to know the irradiance values that I will get. So, I'm trying to convert the lumen (photometric units) given in the datasheet into radiometric units (Watts). The manufacturer does not provide the radiant power in the datasheet, only the luminous flux in lumens.

Thank you for your help.

az32 said:
I'm really struggling with this problem.

I'm sure. Well, I guess you have 2 options- contact the manufacturer, get someone from technical support on the phone, and pester them until you get a radiometric spec; the other option is to measure it yourself with a radiometer.

What a pain... good luck!

## 1. What are the photometric units used to measure retinal irradiance?

The photometric units commonly used to measure retinal irradiance are lux (lx) and candela per square meter (cd/m²). These units take into account the sensitivity of the human eye to different wavelengths of light, which is important in determining the potential harm of light exposure to the retina.

## 2. How is retinal irradiance calculated from photometric units?

Retinal irradiance can be calculated by multiplying the photometric unit measurement (in lx or cd/m²) by the luminous efficacy of the light source, which is the amount of visible light produced per unit of energy consumed. This calculation takes into account the sensitivity of the human eye to different wavelengths of light and provides a more accurate measure of the potential harm of light exposure to the retina.

## 3. What is the recommended safe level of retinal irradiance?

The recommended safe level of retinal irradiance varies depending on the duration of exposure and the specific light source. However, for most light sources, a retinal irradiance of 10 µW/cm² or lower is considered safe for continuous exposure. It is important to note that this is a general guideline and may vary for individuals with certain eye conditions or sensitivities.

## 4. How does retinal irradiance affect eye health?

Exposure to high levels of retinal irradiance can cause damage to the retina, leading to vision problems and potential blindness. This is because the retina is highly sensitive to light and prolonged exposure to high levels of light can cause phototoxicity, which is the damage of cells in the retina.

## 5. Can retinal irradiance be measured at home?

While there are devices available for measuring retinal irradiance, it is not recommended to measure it at home without proper training and equipment. It is best to consult a trained professional, such as an ophthalmologist or optometrist, for accurate measurements and assessments of retinal irradiance.

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