Exposure meter calibration

We may read of a certain external reflected light exposure meter model that it is "calibrated to 12.7% gray". We may be curious as to just what that means, and how is it a description of the "calibration" of the meter.

It actually isn't.

Often, that statement means this, in a digital photography context:


The important point here is that the statement (that is, the story it implies) does not describe the calibration of the exposure meter in an absolute way (as we would have if we tested the meter in a laboratory). Rather, it describes the exposure result that will occur when the meter is used in connection with a camera having a certain significance to its "ISO" setting.

Today, for many digital cameras, the "ISO" setting (by intent of the manufacturer) does not reflect the ISO Speed (saturation) of the sensor. It may instead (perhaps accurately) reflect a different, alternative objective measure of sensitivity, the ISO SOS (Standard Output Sensitivity). This is a "rating" that is 70.7% of the ISO Speed (saturation).

If that is the case for our hypothetical camera, then the story above would end:


Ah, the (in)famous 18%! Pops up in the darnedest places!

Why does the word "gray" appear in the common statement? No real reason. But perhaps because we can also describe the first calibration situation above with these closing verses:

But, if the colorimetric response of the meter is "uniform", we could also say this for those verses of the story:


So we see that the word "gray" has gotten into this already-peculiar story for no good reason. (In fact, there is a tendency for people to describe the an image area of xx% relative luminance as "xx% gray", even if it is pink. And of course, in graphic arts parlance, "15% gray" is a neutral color of 85% relative luminance.)

Regarding the significance of the camera's "ISO" settings. It appears that in modern Canon EOS cameras, the ISO setting is intended to reflect the ISO SOS value. Canon, however, does not say that. Rather, they say that the ISO settings are on the basis of the ISO REI (recommended exposure index), another alternative "sensitivity" rating introduced at the same time as the SOS.

This is not an objective measure of sensitivity. We could not determine the ISO REI for a camera at a particular "ISO" setting in the laboratory. Rather, it is a "rating" that the manufacturer may choose so that, when it is used as the exposure index setting on a light meter with standard calibration, the exposure result, over a range of photographic situations, will be "pleasing" to the user.

What about the "standard" calibration of a reflected light exposure meter? The ISO standard for such meters prescribes a certain calibration (es pressed in a "direct" way, not presuming complicity of any particular camera behavior). But there is a gigantic "wiggle room" in that specification.

Another ISO standard prescribes the "calibration" of integrated automatic expsure systems. It makes a rather "tight" prescription for that calibration.

If a free-standing exposure meter had the corresponding calibration, that would be the one "described" (in a curious way) by the statement at the head of this report (with the number "12.7%" in it).

So it would not be unreasonable to say that the exposure meter of interest had "standard" calibration.

By the way, the actual calibration of a reflected light exposure meter is stated by the factor "K", which is a parameter of an equation that relates:


This of course is "absolute", and does not flow from any story involving some camera.

In closing, I remind the reader that all this relates only to reflected light meters. What about the "calibration" of an incident light meter?

Maybe after breakfast.

Best regards,

Doug

Incident light exposure metering

Before I talk about the "calibration" of incident light exposure meters, I thought it would be best to talk a little about reflected light exposure metering in general.

A reflected light exposure meter of the simple kind observes the relative luminance of the scene. Based on that, and on the exposure index setting (we may here define exposure index as "what we tell the meter is the ISO Speed of the film or camera in use"), it recommends a photographic exposure (that is, a slate of equivalent combinations of shutter speed and f-number).

The technical result of this (in digital photography) is that, on the sensor, the average photometric exposure (the physical phenomenon to which the sensor responds) will be a certain fraction of the "saturation" photometric exposure (the same fraction for any scene).

In terms of the developed image, that means that the average relative luminance will be a certain value (regardless of the scene).

Ther are various ramifications of this, none of them attractive. A common way to describe one of them is:


Another outcome is that for a scene with a relatively low average reflectance, a high-reflectance object (a wedding dress, for example) will receive an over-saturation photometric exposure (that is, will "blow out").

Incident light metering is intended to overcome all these issues. There, the meter determines the illuminance upon the subject from the overall incident illumination.

Based on that, and on the exposure index setting, it recommends a photographic exposure (that is, a slate of equivalent combinations of shutter speed and f-number).

The technical result of this (in digital photography) is that, on the sensor, the photometric exposure for any object patch will be proportional to the reflectance of the object patch.

Typically, the calibration of the meter, in combination with the camera's outlook on "ISO", will result in a scene patch with a reflectance of 100% (the "most reflective 'natural' surface") receiving a photometric exposure just a little shy of saturation.

Thus a black cat (regardless of its context) will receive a very low photometric exposure, and will be "black" in the image; a white cat (regardless of its context) will receive a very high photometric exposure, and will be "white" in the image.

It is interesting to compare this situation with the famous Zone System, a discipline for exposure control. Although we rarely hear it said, its actual objective is also to place the images of objects in the "tonal scale" of the negative or digital image corresponding to their reflectance, albeit in not such a numerically-precise way as with incident light metering.

Often, we use "gray card" metering, in which we take a measurement with a reflected light meter from a neutral target of known reflectance (the "gray card"), and use the indications of that meter to control our photographic exposure. It turns out that this is true incident light metering.

The "calibration" of this "virtual incident light meter" depends on the calibration of the reflected light meter and the reflectance of our target.

Let's work out an example. We assume that the calibration of the reflected light meter, and the nature of the rating of the "ISO" setting of the camera, is as described in the first part of my earlier report. That means that, if the meter regards a target subject to the scene illumination, and we set the photographic exposure to the recommendations of the meter, the photometric exposure for the target (whatever its reflectance) will be 12.7% of the saturation photometric exposure. Simplistically, that means that in the image,m the target will have 12.7% relative luminance.

Now if its reflectance were in fact 12.7%, then this would fulfill our ideal for incident light metering (essentially, fulfill, in a very technical way, the premise of Zone System exposure). Every object in the scene will have a relative luminance in the image equal to its reflectance.

But, we were "taught" (not at this school, bunky) to use a card with a reflectance of 18% for this process. Then, the relative luminance of every object in the scene will be "1/2 stop" lower than its reflectance.

If we don't want that, then we just "bump" the exposure suggestion of the meter by 1/2 stop.

Now, if the camera involved has its "ISO" settings labeled in terms of the ISO SOS (as is apparently so for modern Canon EOS cameras), then (I will spare the reader the mathematical trail), we find that if we use a target with a reflectance of 18% (ah, there it is again), and the reflected light meter has "standard" calibration, every object in the scene will be recorded in the image with a relative luminance equal to its reflectance.

The famous "18% gray card" has been rehabilitated.

In the next part of this series, I will actually talk about the calibration of incident light exposure meters.

Best regards,

Doug

The calibration of incident light expsure meters

An incident light exposure meter measures the illuminance on the subject (or on where the subject will be) and from that, plus the setting of the meter's exposure index dial, delivers a recommended photographic exposure (that is, a slate of of equivalent values of shutter speed and f-number).

The exposure recommendation for any given measured illuminance and exposure index setting is determined by the "calibration" of the meter.

Formally, the calibration is stated by the factor "C", which appears in an equation that relates:


This of course is "absolute", and does not flow from any story involving some camera.

Of course we do not often hear about "C". (Not about "K", either!)

The ISO standard for free-standing exposure meters specifies, for reflected-light meters, a value of "k" (the constant that defines their calibration), with a very broad "wiggle room".

Not surprisingly, it also specifies, for incident-light meters, a value of "C" (the constant that defines their calibration), with a very broad "wiggle room".

We saw in the previous part of this story that a reflected-light exposure meter, regarding a target ("gray card") of a certain reflectance, is in fact a bona fide incident light metering system.

If we assume:

then the exposure recommendation of the incident light meter will be the same as the exposure recommendation of the reflected light meter regarding a neutral target whose reflectance is about 19.6%.

That means, for any given camera situation of how the "ISO" values are reckoned, the exposure recommendations of that incident-light meter will be about 2/3 stop "hotter" than the exposure recommendations of that reflected-light meter regarding a target of 12.7% reflectance.

This can be rationalized as a strategy involving "headroom", which I will save for the next chapter of this series.

I do not endorse any attempt to describe the calibration of an incident-light meter in a way comparable to saying, for a reflected light meter, that it is "calibrated to 12.7% gray" (I don't endorse that either).

By the way, for my only serious free-standing exposure meter, an ancient Miranda Cadius, which has both reflected-light and incident-light modes, the apparent intended calibration constants (as inferred from various tables on the instrument) are:

That means that its incident light mode corresponds to using it in a reflected light mode regarding a neutral target with reflectance 19.6%.

Best regards,

Doug

"Headroom" in expsure metering

We noted in the first article of this series that if:


then, on the sensor, the average photometric exposure (the physical phenomenon to which the sensor responds) will be 12.7% of the saturation photometric exposure (the photometric exposure at which "highlight clipping" occurs).

We can look at that in a different way:

If the average reflectance of the scene is 18%, then for a scene patch with 100% reflectance (the highest possible "natural" reflectance), the photometric exposure on the sensor would be 70.7% of the saturation exposure. That is, in that scenario, there is 1/2 stop "headroom" against clipping for a 100% reflectance object.

We can say it in a different way yet:

If the maximum luminance in the scene is 5.56 (1/18%) times the average luminance, the maximum photometric exposure on the sensor would be 70.7% of the saturation exposure. That is, in that scenario, there is 1/2 stop "headroom" against clipping for the brightest object.

Now, where did the ratio 5.56 come from? It was chosen to represent the greatest ratio of maximum to average luminance over "most" scenes.

Where did the 1/2 stop come from. Well, if we're going to allow a little headroom, that is about the smallest amount worth mentioning. (Do not expect to easily reconstruct this rationale from the standards documents involved!)

The famous "18% assumed average scene reflectance" is the popular way to state that whole story.

Now, in modern cameras, the automatic exposure control system (an integrated, coordinated reflected-light exposure metering system) is not so simplistic as the exposure meter I postulated above. It makes intelligent analysis of the scene, in order to make a good guess as to the maximum luminance there. Thus, the "1/2 stop headroom" seems unneeded.

Accordingly, in many digital cameras (from Canon, for example), the exposure control system was arranged so that, for metered exposure of a typical scene, the average photometric exposure would be about 18% of the saturation exposure (not 12.7%). The 1/2-stop "headroom" had been "burned" in the interest of "more to the right" exposure.

Now, there are two ways that this could be executed, compared to a model based on a "standard" exposure meter calibration and a rating of camera sensitivity based on the actual definition of ISO Speed (saturation):


Now, had the manufacturer chosen "a", there was the risk that persons using reliable external reflected-light exposure meters, and comparing their exposure recommendations for a scene with those made by the camera's automatic exposure system, would conclude that the camera system was inaccurate. Horrors.

Thus they opted for "b".

Now, when sophisticated users realized this, they could hardly accuse the camera manufacturer of fraud, since their rating of the ISO sensitivity of the camera was lower than the actual ISO speed. Curious, but not "fraudulent".

Then, the Japanese camera industry, in a revision of their standard for expressing the sensitivity of digital cameras, introduced a newer measure, an alternative to the ISO Speed (saturation). It was exactly 1/2 stop less than the ISO Speed (saturation). (Fancy that.) This was then taken into the ISO standard, where it became the ISO SOS.

Now let's go back to the world before this happened. Recall that the interaction of the "standard" calibration of a reflected light exposure meter and the use of the genuine ISO Speed (saturation) as the exposure index into the meter gave us what can be considered a 1/2-stop headroom in photometric exposure as protection against "blowout" in the case of a scene with an "unnaturally" high ratio of maximum to average luminance.

But with incident light metering, we do not depend on any assumption about ratio of maximum to average scene luminance to void blowout. The only assumption involved is that no part of the scene exhibits a reflectance greater than 100%. Thus, we do not there need any headroom for safety.

Accordingly, the common calibration of actual incident light meters was made such that we "burn" part of that headroom in the interest of "more to the right" exposure.

Best regards,

Doug

One may wonder why it might be worthwhile to wade through what appears like dense homework. After all, our cameras seem to work, don't they?

Well to a point! Try to take a picture of backlit flower against a bright sky or a scene with a wide range of lighting. You may need to intervene and really know what choices you can make to actually compose with light.

What Doug offers is a hand in hand really gentle walk from what ISO might mean to assumptions made in using other terms along the way. If you have a lightmeter sitting around, get it a new battery if need be and try to follow along.

It will open up great possibilities for control in more challenging shots.

Asher

Well, Fotis,

This thread seems ripe for resurfacing!

Asher

Dear Doug,


I have been bothered for a long time with the question, "if all reflected light meters are calibrated to 12.5% reflectance, why then
there is no product like a grey 12.5% card, or any product with a direct reference to 12.5% reflectance available on the market?"


On the contrary, the only reference relfectance mentioned in every grey card product with known reflectance is 18%.



In my attempt to find out what is going on with the reflected light meters, I tried to derive conclusions out of the final image, as rendered from
a raw file and transformed to tiff with a specific sofware for conversion and viewing.

Although I was able to draw valuable conclusions for the meter behaviour, as well as for the "processing chain" towards the final image, this method
suffers from the fact of introduction of too many variables and parameters that influence the result on the final image, not to mention that every
processing chain is different (different converters and different viewers are generally producing different results, even with "neutral" settings).


Think though about the "pulling the exposure" effect, that you also described in your OP, i.e. the reflected light meter will always suggest a reading
so that the resulted image will be a specific grey tone, whatever the luminance, or reflectance of the photographed scene may be, I thought the obvious:


This consists an intrinsic characteristic of the light meter, so one should be able to determine it without the implication of the whole processing chain
towards the final image, since any characteristics of the camera, lens and sofware must be irrelevent.


In this view, we may be only based on simple measurements of luminance and illuminance and be able to determine this reference reflectance of the meter.



Ideally, we could assume highly accurate measuring instruments, never-the-less, we can also rely on the manufacters' data sheets on characteristics of commercial light meters
to be able to estimate this reference reflectance within certain error margins.


Current manufacturers like Sekonik and Kenko are providing light meter instruments being able to measure luminance and illuminance (reflective and incident).
If we are able to devise a method and assess the error margin, then we can suggest a hilgly possible range of were this reference reflectance lies for these meters.


The outcome of my analysis shows that all comes down to matching the values of reflective and illuminance readings.
The reference reflectance then of the reflected light meters is then provided as:


R* π Κ / Ci


K: calibration constant of reflected light meter (K= 12.5 cd/m^2 for Sekonik, K = 14 cd/m^2 for Kenko)
Ci: calibration constant of illuminance measurement (Ci = 250 lux for both manufacturers)


My estimation is that the respective reference refectances for these two manufacturers seem to lie in the following ranges:

R*(Sekonic) = 15.7% - 16.6%
R*(Kenko) = 16.5% - 17.6%


Obiously the above ranges are close enough to the 18% reflectance to state that both reflected light meters are in line with the 18% reference reflectance concept.



I want also to point out that using these meters at the incident measurement mode with the dome open (lumisphere mode in Sekonic nomenglature) is not appropriate for the determination of reference reflectance,
simply because such a measurement does not constitute even an estimate of the true illuminance falling on a subject flat surface.


In my next posts the full analysis of this consideration will be presented.



Let me appologise for the extensive use of maths, for it is the simplest way trying to describe what I want to say.

Hi, Fotis,

Fotis D. Tirokomos said:

I have been bothered for a long time with the question, "if all reflected light meters are calibrated to 12.5% reflectance, why then
there is no product like a grey 12.5% card, or any product with a direct reference to 12.5% reflectance available on the market?"

Click to expand...

I first have to say that the expression "[exposure meter] calibrated to 12.5% reflectance" doesn't state any objective relationship. If we are going to deal with this rigorously (as you do in your ongoing work), we are going to have to give up "slogans" like that and say just what is actually meant!

And secondly note that there is no unique calibration factor, in either "reflected light" or "incident light meters, prescribed by the applicable international standard.

So what does the phrase about 18% mean? Well, here's a story that involves that number (and I will speak in terms of digital imaging criteria):

The standard exposure equation, based on the midrange value of exposure meter calibration factor in the standard, will, for a scene with an average reflectance of 18%, and a maximum reflectance of 100%, give a photographic exposure recommendation that, if followed, will result in 1/2 stop of "headroom" from saturation at the brightest portion of the scene.

On the contrary, the only reference relfectance mentioned in every grey card product with known reflectance is 18%.

Click to expand...

Dunno about "mentioned", but there are gray cards (admittedly intended primarily for color balance work) with reflectance far from that (one of my favorites has a reflectance of 32%). So perhaps you are speaking of gray cards primarily intended for use in "incident light" exposure metering with a "reflected light" exposure meter.

The outcome of my analysis shows that all comes down to matching the values of reflective and illuminance readings.
The reference reflectance then of the reflected light meters is then provided as:


R* π Κ / Ci


K: calibration constant of reflected light meter (K= 12.5 cd/m^2 for Sekonik, K = 14 cd/m^2 for Kenko)
Ci: calibration constant of illuminance measurement (Ci = 250 lux for both manufacturers)

My estimation is that the respective reference refectances for these two manufacturers seem to lie in the following ranges:

R*(Sekonic) = 15.7% - 16.6%
R*(Kenko) = 16.5% - 17.6%

I think that "implied reflectance" better gives the flavor of it, but I know what you mean!

Indeed, and that comports with the corresponding conclusion drawn from a consideration of the "midrange" values of C and K in the standrd (as I'm sure you know.

Obiously the above ranges are close enough to the 18% reflectance to state that both reflected light meters are in line with the 18% reference reflectance concept.

Click to expand...

I know what you mean, and that is certainly so.

I want also to point out that using these meters at the incident measurement mode with the dome open (lumisphere mode in Sekonic nomenglature) is not appropriate for the determination of reference reflectance,
simply because such a measurement does not constitute even an estimate of the true illuminance falling on a subject flat surface.

Click to expand...

Indeed, an important topic is the acceptance pattern as a function of angle of incidence. For example, if we are interested in the true illuminance on the subject surface (as defined in photometry), then the instrument must have a "cosine" pattern. The usual photographic dual mode meters don't with the dome off (or open), and they don't with the dome in place either. But they are close with the dome in place. (Laboratory illuminometers exhibit very closely a cosine acceptance pattern.)

******

Finally, do note that for many years, the Kodak 18% reflectance gray card (not to be confused with an "18% gray" card, which would have a reflectance of 82%) came with a little note that suggested using an exposure 1/2 stop greater than "suggested" by a reflected light exposure meter reading off the card (thus saying that they recommended the same exposure as would have been indicated with a card of 12.7% reflectance!).

******

You are barking up all the right trees, my friend.

Let me appologise for the extensive use of maths, for it is the simplest way trying to describe what I want to say.

Click to expand...

No need to apologize at all - that is the only way to make clear what we are speaking of! We just need to try to approach that in our prose!

Thanks for your good work on this important area.

Best regards,

Doug

Click to expand...

Hi, Fotis,

I know you know this, but for the benefit of onlookers:

The significance in practice of the relationships you determined for these meters is this:

For these meters, for a certain illuminance upon a scene, the exposure recommendation given by the meter in the incident light mode would be the same as given by the meter in the reflected light mode regarding a test card with a reflectance of about 17% under that same illumination.

Best regards,

Doug

Hi, Fotis,

My only free-standing exposure meter is a Miranda Cadius (the original version).

It has tables on the back relating the meter indication to luminance and illuminance (in the two modes). From those we can, but way of the equations with which you are familiar, determine the (intended) exposure meter calibration constants.

They are:

C= 200 lx
K= 12.5 cd/m²

I leave it to you to determine the implied equivalent reflectance.

Best regards,

Doug

Doug,

Thank you for your insight

Let me comment about what I think some very important issues on this discussion



QUOTE from Doug Kerr:

Indeed, an important topic is the acceptance pattern as a function of angle of incidence. For example, if we are interested in the true illuminance on the subject surface (as defined in photometry), then the instrument must have a "cosine" pattern. The usual photographic dual mode meters don't with the dome off (or open), and they don't with the dome in place either. But they are close with the dome in place. (Laboratory illuminometers exhibit very closely a cosine acceptance pattern.)


I agree that a photometric, flat receptor illuminance meter is bound to have a cosine response.
The commercial incident meters at the "dome retracted" mode I believe are trying to emulate a flat receptor of a true illuminance meter, only when they are frontly lit, because their angular response is not following the cosine pattern accurately, simply because they are not "true" flat receptors.

As a result, I have every reason to believe that at the "dome retracted" mode in frontly lit cases only, these commercial meters provide measurements close to the true illuminance of the light falling on them.

You indicate exactly the oposite: that the dome in place mode is close to a true illuminance measurement (as would have been provided by a true, flat photometric receptor).
Could you clarify this?

Hi, Fotis,

As always, you are "barking up just the right trees".

Fotis D. Tirokomos said:

I agree that a photometric, flat receptor illuminance meter is bound to have a cosine response.

Click to expand...

Quite true for your predicate–an illuminance meter.

However, a dual-mode photographic exposure meter, in its "reflected light" mode (typically that is with no auxiliary dome in place) does not respond to the illuminance on its "flat" organ. Said another way, its flat organ does not exhibit cosine response.

Why?

Because that response is not suitable for observing the luminance of the scene over some arbitrary field of view, which is what we want such a meter to do in its "reflected light" mode.

So its flat organ is made (somehow) to have a "directivity pattern" that results in a reading that approximates the mean luminance of the scene over some arbitrary field of view (which we can describe with respect the the normal to the flat organ—the "aiming direction" of the meter in the reflected light mode).

So now the flat organ is not suitable for luminance measurement (the "incident light" mode, because is doesn't have a cosine directivity pattern.

On the other hand, there are those who feel that a true cosine pattern would not be best for "general" photographic use, the reason being that rarely is the subject surface planar.

Let me discuss that issue for a moment.

If we were photographing a planar subject surface, regardless of its orientation with respect to a line from the camera, and if it were Lambertian, then its luminance (as seen from the camera, or in fact from anyplace else) will be proportional to the illuminance upon it (and its reflectance).

So to plan an exposure, we would want to determine the illuminance of the ambient light, at the subject location, upon a plane parallel to the subject surface. If we had a laboratory illuminometer, we would place it at the subject with its flat organ parallel to the subject surface.

But if the subject surface is not planar (a human face, for example), then there is no single metric that will in all illumination situations predict for us the luminance (for a given reflectance) of all parts of the face.

An empirical solution to this (for the "non-laboratory photographer) is to use an incident-light exposure meter whose directivity pattern is not cosine but which is actually a bit "fatter" (and meter manufacturers jealously guard their decisions as to exactly what pattern will give "the best results in a lot of real cases".

Now back to the "dome". It turns out that a translucent hemispherical dome, when mounted over a flat organ whose response is not cosine but rather as I discussed earlier, will yield a directivity pattern that is not cosine but is useful for "incident light" metering as I discussed just above.

The commercial incident meters at the "dome retracted" mode I believe are trying to emulate a flat receptor of a true illuminance meter, only when they are frontly lit, because their angular response is not following the cosine pattern accurately, simply because they are not "true" flat receptors.

Click to expand...

No. These meters are used for "reflected light" measurement with the dome retracted. There, as I discussed above, we are not interested in determining the illuminance upon the meter receptor. Rather we are interested in the mean luminance of the subject (over some arbitrary, restricted field of view)

As a result, I have every reason to believe that at the "dome retracted" mode in frontly lit cases only, these commercial meters provide measurements close to the true illuminance of the light falling on them.

Click to expand...

No, and that is not what we want in the "reflected light" mode, which is when we retract the dome.

With the dome in place, they almost respond to the illuminance upon the dome (subject to the intentional "deviation" I described above.)

Fun stuff, no.

Again, I assure you that you are asking the right questions, and I enjoy the clarity of your perception.

Best regards,

Doug

Hi, Fotis,

Suppose we take a genuine illuminometer (which truly measures the illuminance upon the plane of its organ (which is likely flat) and face it toward the center of some "scene" we plan to photograph.

What governs the instrument reading? Well, it is proportional to a weighted average of the luminance of the entire scene (the entire hemisphere of it) (as seen from the instrument location), the contribution of each little element being weighted by the cosine of its angle off the normal to the instrument.

Now, if we plan to use classical reflected light exposure metering (for better or worse) to choose a photographic exposure for our shot of some portion of the scene (which we will frame using whatever lens and focal length we choose), what metric would we like to have from the measurement stage of the expsure meter?

A. Ideally: the mean luminance of the portion of the the scene that will be in the shot.

B. Less ideally, but the result of using a "typical" reflected light exposure meter: the mean luminance of the portion of the scene taken in by the "field of view" of the exposure meter. Our hope is that this is in fact not very different from what we really want to know (A).

Now, with respect to B, the typical reflected light exposure meter does not have a sharply-defined field of view. Rather, it typically has a response that is fairly uniform over a range of angles of the different "elements" that are observed, and then falls off rather gradually—reaching a very low value by the time we get well outside the likely field of view of any camera setup we might be using.

But this is dramatically different from a response that is proportional to the cosine of the angle off-axis up to 90° in any direction—the response of an actual illuminance instrument.

So this is why the response of a reflected light exposure meter (or a dual-mode meter in the reflected light mode) should not make that instrument indicate the illuminance upon its organ.

Best regards,

Doug

Hi Doug,

Thank you for your insight.

There is a misunderstanding, I measure the reflected light with a separate spot meter, I don't uncover any receptor

You can take a look at the layout of the 3-mode actually, light meter I use:

http://www.sekonic.com/Products/L-758D/Overview.aspx


You can check out the three distinct modes of operation:

1) Reflected light using the separate lensed arrangement to take measurement of luminance, within a cone of 1 degree.

2)luminance measurement frontly lit retracted dome configuration, Sekonic manual outlines the conversion table of readings to illuminance values, based of cource on the equation:

Es = 250 lux/ 100* 2^(EVmi)

EVmi: meter reading at dome retracted mode

3) Incident light estimations based on the spherical diffuser (they call it the "lumi-sphere" mode)

I hope it is clear now

Doug Kerr QUOTE:
C= 200 lx
K= 12.5 cd/m²

I leave it to you to determine the implied equivalent reflectance.


Dear Doug,

you spoiled the fun (!) for, you have already given away the correct answer, 19.6%, for your Miranda Cadius' implied reflectance (I fully agree with this term, I am adopting it).

Yet, the correct answer is also 15.7% for the implied reflectance of the same reflected light meter, if you use any other illuminance meter with Ci=250 lux.

The fact that for the assessment of an intrinsic characteristic of a (reflected light) meter is relied upon an (ideally, perfect) illuminance meter, still getting different results for the implied reflectance R*, depending on the values of Ci factor is quite confusing.


In order to alleviate this confusion and uncertaintly we have to resort to a alternative, yet equivalent consideration that is not infuenced by the (free within limits) choice of
factor Ci.




Had an idea though and put it forward (I do appologize for the quite extensive use of maths, but it is the only way to convey exactly what I want to say)




Such a consideration may primarely take into account the actual rensponse of the sensor itself as a result of the light energy stimulus. i.e. , the Exposure H = E . t, of the sensor plane (with E the sensor plance illuminance and t the exposure time).



I intent to take here the results with "ready made formulae" for which I provide the full reasoning in the section justfication "ANALYSIS" for clarity for the reader afterwards.



In my justification ANALYSIS section, will be shown how we can alternatively provide an expression of the same physical quantity, the sensor exposure H, based on reflected light readings (H = Hr) and, alternatively, based on illuminance meter readings (H = Hi) as,



H = Hr = b/S . K, according to the subject surface reflected light metering process (setting the camera according to the meter readings)


H = Hi = 1/π . b/S . Ci . R , according to the subject surface illuminane metering process (setting the camera according to the meter readings)




Hr: resulting sensor exposure H, when setting the camera according to the reflected light meter readings


Hi: resulting sensor exposure H, when setting the camera according to an illuminance light meter readings


S: ISO speed set on the meters


b: a factor depending on the actual lens characteristics (more info in the ANALYSIS)





The first relation is essentially a constant value, depending only on K (not luminance nor reflectance) and therefore constitutes the manifestation on sensor exposure H of the implied reflectance R* of the reflected light meter, therefore we can denote this exposure value as H_R*:


H = Hr = H_R* = b/S K



The second relation reveals a mostly important feature: as longs as we set our camera according to the readings of (any) illuminance meter, the resulting sensor exposure is linearly proporsional to the subject surface reflectance value R, bounded between certain limits:



Hi_min = 0 (for R = 0)


Hi_max = 1/π . b/S . Ci (for R = 1)



The value Hi_max is the resulting stimulus to the sensor, as determined by any specific (Ci) illuminance meter, for a total white subject surface (R = 100%)



If we assume now the true saturation exposure H_sat for the particular sensor we use, we may also assume that,


H_sat = H_sat(S)


just to emphasize that the sensor saturation exposure is a function of the True ISO speed S of the sensor.


Then, from the linearity of exposure with reflectance R we get:



H_R* / H_sat(S) = R*


The last relationship, constitutes a straight forward (without any involvement of a separate illuminance meter) derivation of the implied reflectance R* of our reflected light meter, only depending on characteristics of the sensor (H_sat) , lens and our actual meter (H_R*).


Experimentaly, we can even take away the influence by the lens in fron of the sensor and measure R* for a particular sensor, by regulating the iight power on a uniformly lit grey subject surface so as carefully define the clipping point of the sensor (set at the true ISO speed, S, same as the meter), taking measuments of the light along the process.
Susequently we gradually decrease the light power until we get the tonality of H_R* on our image file observed.

Then we compute:


R* = 2^(EV_R*) / 2^(EV_sat)


with EV_R* - EV_sat is the measured decrease of the light power from the actual clipping point down to the point of rendering the corresponding tonality to H_R*.







Alternatively, let us compare the actual saturation exposure H_sat(S) for the true ISO speed S of the sensor and the maximum sensor exposure Hi_max, as determined by any random illuminance meter (Ci).

We are free to assume a factor x, in the sense that:


Hi_max = x . H_sat(S)


We understand that, to regard this illuminance meter (Ci) as successful in exposing this particular sensor, then x < 1 to avoid saturating the sensor, but on the other hand x must be adequately close to 1 so as to ideally translate "white" as "white" not white as grey.



From Hi_max = 1/π . b/S . Ci the above yields:



H_sat(S) = 1/π . b/S . Ci/x




We may define


Ci_sat = Ci/x



as the illuminance meter that would ensure the exact exposure Hi_max = H_sat(S) for the particular sensor at the particular True ISO setting.
The illuminance meter Ci_sat is one and only per sensor, per True ISO setting, since H_sat(S) is a pure characteristic of the sensor, at the particular True ISO speed setting S.

Whatever random illuminance meter Ci we may use, the factor x will be accordingly adjusted to provide the constant Ci_sat = Ci/x.



We then have the following relations valid:


R* = H_R* / H_sat(S)


H_R* = b/S K


H_sat(S) = 1/π . b/S . Ci_sat




therefore



R* = π K / Ci_sat



Consequently we can see that the implied reflectance R* can be expressed as a function of the reflected light meter itself via its parameter K, but it is also influenced by the saturation characteristics of the medium (sensor) at the particular true ISO speed settings we are looking into.

This is an acceptable outcome for me.


What remains is the estimation work to define the range of values of factor x.



I am very sorry for the length of this post.

Justification ANALYSIS (for previous post)


Let me provide for the sake of clarity to the reader the analysis of the statements I made:



Let us assume a flat surface as a subject, having a tonality of grey (to make it simple, no color is foreseen) and reflectance R, that is uniformly-frontly lit, being also an ideal - Lambertian - difusser.

This subect surface fills up the frame and sensor of a camera - lens system.

Sensors (or films) are responding to the amount of light energy falling on them and the physical measure to describe this light energy is the sensor Exposure H (in Lux sec), that is expressed by the equation:



H = E . t


E: sensor illuminance (lux)
t: exposure time of the sensor (shutter speed or flash duration, in sec)


The sensor illuminance E is related with the corresponding subject luminance Ls that is producing it, as:


E = b / A^2 Ls


b: expresses a set of parameters related to lens characterstics (transmittance, flare, vignetting) and geometry (distance, angle of view, focal lenght). We assume a certain configuration setup that stays unchanged at all times so that b remains constant and we expect to be cancelled out somewhere in the course of our process.

A: the lens relative aperture number (f-stop)
Ls: the subject surface luminance (brightness) (cd / m^2)




Combining the above, we get for the sensor exposure H:




H = b / A^2 t Ls



We may substitute, 2^(EVc) = A^2 / t , denoting as EVc the settings (f-stop - shutter speed) on camera and we get,




H = b 2^(-EVc) Ls



The last relation relates the cause (subject surface luminance Ls) with the effect (sensor exposure), via the parameters of the lens used, as well as the camera settings. Evidently, for constant camera settings EVc, the sensor exposure is directly proportional to the subject luminance Ls.




Let us now come to our reflected light meter in subject


This instrument performs a measurement of the subject surface luminance Ls and translate this measurement to proposed values EVmr output to the meter (meter reading),
in a clear prescribed by the ISO standards way, the light meter equations:



2^(EVmr) = S / K Ls or equivalently Ls = K/S 2^(EVmr)


EVmr: output values of the reflected light meter (f-stop, shutter speed)
S: ISO speed, as set to the light meter
K: reflecte light meter factor (K= 12.5 cd/m^2 for Sekonic, K = 14 cd/m^2 for Kenko)
Ls: subject surface luminance





We can now express the sensor exposure H, substituting for Ls, the corresponding meter readings EVmr:




H = b/S K 2^(-EVc) 2^(EVmr)



Setting the camera to the light meter reading, i.e. EVc = EVmr, the above yields:



H = Hr = b/S K


This constant, characteristic sensor exposure Hr is the "medium grey tone" rendered always, according to the readings from this particular reflected light meter.


Trying to determine from this reflected meter alone, which is the implied subject surface reflectance which yields this characteristic "medium grey" Hr is totally futile.



Let us now consider the use of an independer, illuminance meter


This can take independent measurements of the true illuminance Es ( light power- or flux - per unit area) of the light falling on our subject surface.

We can use a separate, flat receptor illuminance meter to measure the illuminance Es, by placing it directly on and parallel to the flat subject surface.




An illuminance meter measures Es and can translate this measurement to output values - suggested camera settings, the meter reading EVmi according to the meter equation:




2^(EVmi) = S Es / Ci or equivalently Es = Ci / S 2^(EVmi)


S: ISO speed, set to the illuminance meter
Ci: the illumince meter factor (Lux)



We can associate the measurement of Es with the resulting exposure H of the sensor itself, introducing the reflectance R of our - ideal difusser - flat subject surface, for it holds that:



R = π Ls / Es


Ls: luminance emerging from our ideal diffusing subject surface
Es: illuminance from flux falling on the subject surface



therefore from H = b 2^(-EVc) Ls, we get H = b 2^(-EVc) R/π Es



The above states that for a given camera setting EVc, the sensor exposure is proportional not only to the illuminance Es, but also to the reflectance R of the subject surface.



We may substitute Es with the equivalent output values EVmi of the illuminance meter and then we can express H as:




H = 1/π . b/S . Ci R . 2^(-EVc) 2^(EVmi)



It is interesting to note that if we set the camera to the meter reading, i.e. EVc = EVmi - our normal practice -, means that any changes in the illuminance Es are compensated by EVc and therefore the
sensor exposure becomes un-influenced by the illuminance changes, yielding:



H = Hi = 1/π . b/S . Ci . R

Again, I'm sorry Doug for putting all this stuff here, I don't have a simpler way to make myself clear.

I hope it is not boring or irritating.

If so, let me know to delete it