{"id":4020,"date":"2009-12-14T00:00:19","date_gmt":"2009-12-14T05:00:19","guid":{"rendered":"http:\/\/www.olino.org\/us\/?p=4020"},"modified":"2015-12-31T16:29:43","modified_gmt":"2015-12-31T15:29:43","slug":"sp-ratio","status":"publish","type":"post","link":"https:\/\/olino.org\/blog\/us\/articles\/2009\/12\/14\/sp-ratio\/","title":{"rendered":"S\/P-ratio"},"content":{"rendered":"

\"lli_bv-high-bay-industrial-led-fixt-48-pcs-cree_s_and_p_spectra_at_1m_distance\"<\/a>This article explains about the S\/P ratio. At very low ambient light levels this ratio indicates the maximum gain in efficiency one can obtain just by using different receptors in the human eye.
\nThe teaser image shows the spectrum of the light of a streetlight, and also the two human eye sensitivity curves; the daytime (red) curve lower in sensitivity than the nighttime (black).
\n<\/p>\n

Rods and cones in the eye<\/h3>\n

The human eye makes use of a.o. rod and cones. Rods are different than cones, and also more sensitive. Some characteristics of both:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
parameter<\/th>\nRods<\/th>\nCones<\/th>\n<\/tr>\n
Location (roughly)<\/td>\nSituated in the eye\u2019s retina<\/td>\nSituated in the eye\u2019s retina<\/td>\n<\/tr>\n
Location (more precisely)<\/td>\nAround the fovea, the remainder of the retina.<\/td>\nMainly, and in high numbers, inside the fovea. It is there where most details are perceived.<\/td>\n<\/tr>\n
Number<\/td>\n120 million<\/td>\n6-7 million<\/td>\n<\/tr>\n
Optimal light level (qualitative)<\/td>\nLow (night, moonlight, twilight)<\/td>\nHigh (daytime)<\/td>\n<\/tr>\n
Optimal light level (quantitative)<\/td>\n< 0.001 cd\/m2<\/sup><\/td>\n> 0.6 cd\/m2<\/sup><\/td>\n<\/tr>\n
Sensitivity (qualitative)<\/td>\nHigh, bad for color perception, no red, less details visible, good for diffuse light<\/td>\nLow (lots of light needed), perfect for colors, details well visible, good for directly incident light<\/td>\n<\/tr>\n
Sensitivity (quantitative)<\/td>\n1700 lm\/W<\/td>\n683 lm\/W<\/td>\n<\/tr>\n
Speed (qualitative)<\/td>\nfast<\/td>\nslower (20 ms slower with comparable light levels)<\/td>\n<\/tr>\n
Overview eye<\/td>\n\"rods_cones_eye\"<\/a>Click on the image for a zoom. Coming from this site<\/a>. The image well indicates were the retina is and the position of the rods and cones.<\/td>\n<\/tr>\n
Rods and cones<\/td>\n\"rods_cones\"<\/a>Two cones amid a number of rods.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The rods are used primarily with low ambient light levels; when there is a lot of light they do not function. So when the light application is about generating light in low light ambient conditions (night time, twilight, moonlight) then one can make optimal usage of rods.<\/p>\n

The eye sensitivity curves<\/h3>\n

As indicated there is a difference between the rods and the cones. The eye (spectral) sensitivity curves indicate how sensitive both are for the different colors (or, wavelengths) of light.<\/p>\n

\"s_and_p_spectra\"<\/a><\/p>\n

(Spectral) sensitivity curves of the human eye<\/em><\/p>\n

It is clear that rods (under photopic light conditions) are sensitive for blue-green light and not for red light. Their sensitivity is clearly higher, maximally 1700 lm\/W and for cones this maximum value is 683 lm\/W (photopic light conditions).<\/p>\n

When developing light for really low ambient light conditions (parking garages, night illumination) then it is more efficient to generate light with the majority of its energy in the scoptopic sensitivity area of the human eye. It is to be compared with moonlight, which is very cold white (blueish white). The human eye is during its evolution completely adapted to it.<\/p>\n

Visually useful light<\/h3>\n

Take a randomly selected lamp. This gives light with a certain spectrum (power spectrum or also called color spectrum). This spectrum can be weighted against the spectral eye sensitivity curve.
\nAll color spectrum meters, giving their resulting light values in lux, are calibrated to the daylight eye sensitivity curve (the photopic light intensity curve). So the reported lux value is valid when cones are working well, and these work well with high or at least sufficient ambient light conditions.
\nFor low levels of ambient light one needs to weigh the spectrum of the illuminant against the scotopic (low light intensity) eye sensitivity curve, or maybe a combination of both. In the latter case this is called mesopic light level, where both the rods as well as the cones are active.<\/p>\n

A publication<\/a> dealing with this issue is coming from ASSIST. This publication works with a certain plan consisting of steps to be executed one after the other to come to a comparison between lamps. An example of a comparison: the are sodium lamps used for night illumination, which emit light with a certain color spectrum, which results in yellowish light. When using an other lamp emitting ligh with much more blue content (which has a better match with the rod\u2019s sensitivity), then less light is possibly needed (compared to photopic\/daylight levels). See below a short description of the steps.<\/p>\n

1. <\/strong>the publication starts with mentioning recommended illumination values (in lux) on different types of public roads. One chooses the right type of public road and reads the recommended (minimum) illumination value.
\n2. <\/strong>this illumination value in lux is computed into a luminance (in Cd\/m2<\/sup>), indicating an intensity (and it are intensity-differences that are actually perceived or seen by the human eye). So an incident amount of light energy in lux is converted into luminance in Cd\/m2<\/sup> (one uses an estimate for the reflection factor of the pavement, and one assumes a perfect diffuse surface). Since the recommended minimum lux values are determined on the photopic eye sensitivity curve, the resulting luminance calculated is also based on the photopic sensitivity curve and is called photopic luminance.
\n3. <\/strong>Once the needed photopic luminance value is known, the illumination level is known: either scotopic (<0.001 Cd\/m2<\/sup>) or mesopic (in between), or photopic (>0.6 Cd\/m2<\/sup>). When in the scotopic or mesopic level, then one have to take into account the human rods and their higher sensitivity as well.<\/p>\n

3a. <\/strong>This can be done by using a table presented in the publication. In the first row the requested photopic sensitivity is given. Then the S\/P ratio of the used illuminant needs to be known. As an example a high pressure sodium lamp is taken, with a known (low) S\/P ratio of 0.63. This means little green-blue so not so efficient for the rods. The table gives, with the S\/P ratio known and the requested luminance value, the unified luminance. This is a luminance that is taking both effect of rods and cones into account. It will only take the effect of rods into account when in scotopic or mesopic light conditions.
\n3b.<\/strong> The unified luminance is known. If now a lamp is taken with a higher S\/P ratio, then starting with the needed unified luminance, one can find the belonging photopic luminance (with the known S\/P factor) and then it is seen that less photopic luminance is needed to generate the same unified luminance. This is the gain! A lamp with a high S\/P ratio and when used in scotopic or mesopic light conditions, does need less photopic luminance to get to the requested unified luminance.
\n3c. <\/strong>This new, lower photopic luminance, can be calculated back to the needed illuminance value (using the same reflection value) and the result is that less lux are needed!<\/p>\n

The relation of visual useful light is as follows: at low light level conditions a high S\/P ratio can lead to better use of the human eye sensitivities and eventually a saving on the light illumination values (when expressed in photopic condition) can be possible. However the S\/P value is needed as an input.<\/p>\n

The S\/P ratio and its determination<\/h3>\n

The lamps measured by OliNo have, since a certain date, the S\/P ratio as parameter defined. The next graph is given as example.<\/p>\n

\"philips_halogeen_35w_gu10_s_and_p_spectra_at_1m_distance\"<\/a><\/p>\n

The power spectrum, scotopic and photopic sensitivity curves and the resulting weighted night and daylight power spectra (last ones at 1 m distance).<\/em><\/p>\n

First in blue the power spectrum of the light of the light bulb concerned. It is a relative measure (assume linear scale) and does not have an y-axis as reference.
\nA black dashed line shows the scotopic eye sensitivity curve. The dashed red line shows the photopic eye sensitivity curve, which are both connected to the left y-axis.
\nThe black line is the scotopic power spectrum (weighted) what results when the power spectrum is weighted against the scotopic sensitivity curve.
\nThe red line in the photopic power spectrum (weighted) results when the power spectrum is weighted against the photopic sensitivity curve.<\/p>\n

The surface below the scotopic power spectrum, divided by the surface below the photopic spectrum, gives as a result the S\/P ratio. For this example lamp it is 1.25.<\/p>\n

The example lamp taken was a halogen lamp. Its light has a lot of red and very little blue. As the sensitivity of the rods is about 3 times higher than that of the cones, still with little blue and a lot of red the resulting S\/P ratio was still more than 1.0, meaning still some more efficiency is expected when rods use this type of light.
\nIt is clear that the more blue is in the illuminance\u2019s light, the higher the S\/P ratio is and the more benefit can be obtained when these light is used in low ambient light confitions.
\nNow the very first image can be looked at and understood.<\/p>\n

The application of the S\/P ratio<\/h3>\n

One can beneficially use the S\/P ratio when a lamp with high S\/P ratio is used in scotopic or mesopic light conditions. Possibly street lighting, especially where it concerns only pedestrian of bicycle traffic, as they do not carry headlights that might generate too much light by themselves to make the mesopic or photopic light condition invalid. In cases where photopic or mesopic light conditions are valid, then a lamp with high S\/P ratio would make more use of the higher sensitivity of the rods of a human eye and therefore the originally requested (photopic) illumination values can be lower. The steps outlined by ASSIST offer a possibility to select higher S\/P ratio lamps and compare these with already existing situations, as see what gain is possible.
\nIn this article an other possible approach is given to use the tables in the ASSIST publication, which can be easier.<\/p>\n

Determine the requested illumination level and luminance<\/strong><\/p>\n

What we need is a specification of what illuminance value is needed. This can be retrieved from norms. As an example use the ASSIST publication<\/a>, containing a table with minimum illumination levels for streetlighting. Assuming a local street, with low pedestrian traffic, an average reflection of 10 % which is also assumed diffuse, then the illuminance value is computed into a luminance value as follows:<\/p>\n

\"\"<\/a><\/p>\n

This computed luminance is the photopic luminance, not taking into account the possible higher sensitivity of the rods in the human eye. This photopic luminance is correct when in photopic light conditions, bit when in lower light conditions one can make a beneficial effect of the higher sensitivity of the rods.<\/p>\n

Evaluate the luminance and determine the unified-luminance<\/strong><\/p>\n

When the desired luminance falls into the scotopic (< 0.001 Cd\/m2<\/sup>) or in the mesopic light level (> 0.001 Cd\/m2<\/sup> en < 0.6 Cd\/m2<\/sup>) then it is useful to compute the found illuminance into a unified luminance. The S\/P ratio of the lamp is needed for that.
\nNote that at requested luminance values of at least 0.6 Cd\/m2<\/sup> we are in the so called photopic light level and then rods do not function well meaning no benefit can be obtained from using the higher sensitivity of these rods over the cones; the unified luminance is then the same as the photopic luminance.
\nWe start with the photopic luminance that is requeted and the S\/P ratio of the lamp, and determin the unified luminance. This is the real experiences luminance (intensity) by the human eye. The computation is as follows:<\/p>\n

\"\"<\/a><\/p>\n

where:<\/p>\n

P is the photopic luminance and
\nS is the scotopic luminance,
\nthis latter can be computed with the S\/P ratio:<\/p>\n

\"\"<\/a><\/p>\n

When the S\/P ratio > 1, then the computation will give an Lunified<\/sub> that is bigger than the P. This is correct, as we are in a scotopic or mesopic light level confition and here the experienced intensity of luminance is higher than a sole computation on photopic levels does make us believe.<\/p>\n

Take the unified luminance the same as the requested limunance<\/strong><\/p>\n

We calculated an Lunified<\/sub>, and in the event the S\/P ratio > 1, the Lunified<\/sub> will be bigger than P. So we have more luminance than needed\/requested, and can go for less. There is in this potential for a saving in driving and power consumption of the lamp. It is all about the perceived luminance, and therefore we need to compute with the unified luminance.
\nSo by putting Lunified<\/sub> equal to the requested or recommended value, one can compute back what is needed for P (with the S\/P ratio) and then compute back what needed illuminance values are needed.<\/p>\n

Use the ASSIST table for determination of the P and Ev, via the S\/P and Lunified<\/sub><\/strong><\/p>\n

ASSIST table nr 3 can be used. As the equation to compute Lunified<\/sub> cannot easily be used to compute P from Lunified<\/sub>, it is easier to use the table made by ASSIST, that contains many computed values already.<\/p>\n

Example: having a lamp with S\/P ratio of 2.05, and a requested P of 0.1 Cd\/m2<\/sup>. The table indicates with these two inputs an Lunified<\/sub> of 0.1568 Cd\/m2<\/sup> (which could also have been computed with the earlier given equation for Lunified<\/sub>). Since only 0.1 Cd\/m2<\/sup> is needed, one can follow the row of the chosen lamp with S\/P ratio of 2.05 to the left until Lunified<\/sub> is equal to 0.1, and read at the top row what P is equivalent herewith.<\/p>\n

\"spratio_use_table\"<\/a><\/p>\n

A part of table 3 from the ASSIST publication, and the way to come to the really needed P.<\/em><\/p>\n

The left column shows S\/P ratios, and the first horizontal row shows the P values. It becomes clear that 40 % reduction can be obtained; only 0.06 Cd\/m2<\/sup> for P is needed to get an Lunified<\/sub> equal to 0.1 Cd\/m2<\/sup>, when using a lamp with an S\/P ratio of 2.05 and with the mentioned low light levels!
\nWith the 0.06 Cd\/m2<\/sup> for P the illuminance value can be computed which also results in a lower value.<\/p>\n

Amount of saving<\/h3>\n

The amount of saving depends on:
\nThe S\/P ratio: the higher this ratio the more possible saving, as the light generated is in a frequency band where the rods are sensitive.
\nThe requested light level. The lower the requested level (so the more towards the scotopic light level, or otherwise the farther away from photopic light levels) the more the rods function and the more benefit can be made from their higher sensitivity.
\nNote: it is important that a certain low light level is not disturbed by sudden high intensity light spots. For instance on a low traffic road for cars, even though the normal light level is low, when a car passes then the headlights disturb the low light level considerably and for the human eye it needs to adapt to this higher light level and after the car has passed, it needs to adapt back to the low light level again (which, depending on the intensity of the head lights and the age of the person, can take many minutes).<\/p>\n

Beware on the effect of dimming<\/h3>\n

When lamps are dimmed, their color temperature can change as well. This means the spectrum changes and herewith the S\/P ratio. For LEDs, the method of dimming (amplitude dimming opposed to PWM dimming) can have a different impact on the color temperature. These effects can be measured so that the S\/P ratio is known also when lamps are dimmed.<\/p>\n","protected":false},"excerpt":{"rendered":"

This article explains about the S\/P ratio. At very low ambient light levels this ratio indicates the maximum gain in efficiency one can obtain just by using different receptors in the human eye. The teaser image shows the spectrum of the light of a streetlight, and also the two human eye sensitivity curves; the daytime […]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[12],"tags":[68],"_links":{"self":[{"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/posts\/4020"}],"collection":[{"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/comments?post=4020"}],"version-history":[{"count":6,"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/posts\/4020\/revisions"}],"predecessor-version":[{"id":23807,"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/posts\/4020\/revisions\/23807"}],"wp:attachment":[{"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/media?parent=4020"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/categories?post=4020"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/olino.org\/blog\/us\/wp-json\/wp\/v2\/tags?post=4020"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}