hwo to prove EV = SV + BV = TV + AV ?

[willis zen]

Is there someone know the root cause of the equations:EV = SV + BV = TV + AV?
after searching some meterials,
I have seen below blog: http://brayebrookobservatory.org/Bra...CALC_HIST.html
here the BV is luminance or illuminance ?
what's the range of BV ?
how to deduce the SV = log[ISO/math.PI] / log(2) ?
here SV + BV = TV +AV should all has been calcuted by Log. so the real relationship between the SV, BV, TV, AV should be multiple.

thank you all in advance.

[IzzieK]

A long read for me in the middle of the morning...I'll have a go at understanding the article later on when I am more awake...

Is there someone know the root cause of the equations:EV = SV + BV = TV + AV?
after searching some meterials,
I have seen below blog: http://brayebrookobservatory.org/Bra...CALC_HIST.html
here the BV is luminance or illuminance ?
what's the range of BV ?
how to deduce the SV = log[ISO/math.PI] / log(2) ?
here SV + BV = TV +AV should all has been calcuted by Log. so the real relationship between the SV, BV, TV, AV should be multiple.

thank you all in advance.

[willis zen]

oh, sorry for distrubing your sweet dreams.
ok... it's time wake up now.

[chauncey]

I took a quick glance at the treatise and concluded that it held all the interest of college kids
pondering the meaning of it all at the local ratskeller over a pitcher of whatever.

MOD EDIT - I don't think it is helpful to be so dismissive of the first post from a new member. It may not be of interest to all of us, but it is to the person who made the post. I think we need to respect that and respond accordingly.

[Venser]

I'm looking at that equation and V is common to all terms. Wouldn't it make sense to simplify?
You're now left with the following:
E = S + B = T + A

[revi]

I'm looking at that equation and V is common to all terms. Wouldn't it make sense to simplify?
You're now left with the following:
E = S + B = T + A

In the original, the variables are named Ev, Sv, Bv, Tv and Av, so the 'V' is not a separate variable..

As to the original question: have a look at this wiki page (referenced in the blog page from the original post). Note that there are two fudge factors (sorry, "calibration constants" ) involved to get the system to work.

What it boils down to is that given a brightness and sensor/film sensitivity, you can calculate which combinations of aperture and speed settings would give you the proper exposure value. The example given in the blog cited talks about photographing the moon through a telescope.

Note that the equation as such cannot be proven, in that only certain values for the variables will work. It's a tool for use with the proper tables and a lightmeter (or any other way to know how much light you have to work with) to get a decent exposition (basically: my meter tells that with this film I have to pick a shutter speed/diaphragm combination from that series under the current light conditions)

[DanK]

Willis,

The logarithmic and multiplicative expressions they give are equivalent. you can express the relationships either as products of the variables or as the sum of the logs of those variables. Makes no difference.

This boils down to something much simpler than the article. The brightness of an image will depend on the brightness of the light source, the aperture (which affects how much light you let in), the shutter speed (which affects how much light you let in), and the sensitivity of the receptor, whether it be film or the sensitivity of a digital sensor. The last could be put on any scale, but conveniently, it is traditionally put on a scale (ISO now, ASA in the old film days) in which a doubling of the variable indicates a doubling of sensitivity.

The multiplicative nature of the relationship is clear if you take a simple example. Suppose that you have a sensor at ISO 100, you set the aperture at f/8, and you set the shutter speed at 1/200. Now suppose that this is the ideal exposure for some given level of brightness of the subject. Now, double the time that the shutter is open, 1/100. Twice the light is let in. Now, open the aperture one stop, to f/5.6. That also doubles the light, so the two changes increase the light by 2 x 2 = 4 times.

The only thing that complicates this, which is explained in a rather obscure way in the article, is that doubling the physical size of the aperture increases the amount of light by 4 times, not twice. The reason is that the area of a circle--which determines the amount of light coming in--is pi r ^2. This is why f/stops are not integers. To double the light, you have to increase the radius of the aperture by the square root of 2, approximately 1.4. That's why an increase of "one stop," which increases light by a factor of two, is a multiplicative change of 1.4 in the f/stop numbers. Hence the sequence of stops: 1.4, 2, 2.8, 4,

[William W]

Willis,

Welcome to CiC,

Re your question - what Remco and Dan wrote.

I thought that I recognized the Formula as part of the "APEX System" - reading the thread through confirmed that thought.

The "APEX System" never really took hold in Photography.

Probably the wiki link to "APEX System" is a good source for background information and a good explanation for you.

WW

[willis zen]

Dear Revi,
thanks for your good answer.
I am absolutly aggre with your opinion: "
Note that the equation as such cannot be proven, in that only certain values for the variables will work........"

For these days, I just wrote an algorithm to do center average metering for a smart phone.
I think I have finish it 50%. due to the samrt phone, the aperture is fixed. so, what should I do was, according the liminance of sensor ouput to decide the sensor shutter speed / Gain.
at first, I want follow the APEC system to calculate it. but I was fail. so, I follow an basic rule, aperture, shutter speed, gain all will effect the image brightness. I adjust the relationship all of them according the brightness and get the exactly the shutter/gain I want.

[willis zen]

Willis,

Welcome to CiC,

Re your question - what Remco and Dan wrote.

I thought that I recognized the Formula as part of the "APEX System" - reading the thread through confirmed that thought.

The "APEX System" never really took hold in Photography.

Probably the wiki link to "APEX System" is a good source for background information and a good explanation for you.

WW

thanks, William

[willis zen]

thank for your good answers, Dan.

Willis,

The logarithmic and multiplicative expressions they give are equivalent. you can express the relationships either as products of the variables or as the sum of the logs of those variables. Makes no difference.

This boils down to something much simpler than the article. The brightness of an image will depend on the brightness of the light source, the aperture (which affects how much light you let in), the shutter speed (which affects how much light you let in), and the sensitivity of the receptor, whether it be film or the sensitivity of a digital sensor. The last could be put on any scale, but conveniently, it is traditionally put on a scale (ISO now, ASA in the old film days) in which a doubling of the variable indicates a doubling of sensitivity.

The multiplicative nature of the relationship is clear if you take a simple example. Suppose that you have a sensor at ISO 100, you set the aperture at f/8, and you set the shutter speed at 1/200. Now suppose that this is the ideal exposure for some given level of brightness of the subject. Now, double the time that the shutter is open, 1/100. Twice the light is let in. Now, open the aperture one stop, to f/5.6. That also doubles the light, so the two changes increase the light by 2 x 2 = 4 times.

The only thing that complicates this, which is explained in a rather obscure way in the article, is that doubling the physical size of the aperture increases the amount of light by 4 times, not twice. The reason is that the area of a circle--which determines the amount of light coming in--is pi r ^2. This is why f/stops are not integers. To double the light, you have to increase the radius of the aperture by the square root of 2, approximately 1.4. That's why an increase of "one stop," which increases light by a factor of two, is a multiplicative change of 1.4 in the f/stop numbers. Hence the sequence of stops: 1.4, 2, 2.8, 4,

[IzzieK]

oh, sorry for distrubing your sweet dreams.
ok... it's time wake up now.

When I came in and saw your post, it was at on Page 3 with some 17 views but no response. I replied to it so that it will go to Page 1 so that more members will notice it. I hope you appreciate what I did instead of....

Have a nice day.

[willis zen]

When I came in and saw your post, it was at on Page 3 with some 17 views but no response. I replied to it so that it will go to Page 1 so that more members will notice it. I hope you appreciate what I did instead of....

Have a nice day.

yes. got it. all the people @CiC are real good guys.
Thank you very much .