A (dumb) question regardind relative DOF

[sury]

I know that A900 has shallower DOF compared to A700. Would someone please explain if the equivalent (to A700)
DOF is reduction by the crop factor or the square of the crop factor or by some other factor? What I want to know
the equivalent (to A700) value if A900 setting is say f8.

Thanks in advance.

with best regards,
Sury

[David Kilpatrick]

The different is 1.5 stops. For the same depth of field at f8 on the A700, the A900 must be set to f/13 or f/14.

David

[sury]

David,
Thank you. If you don't mind, would you explain how you arrived at 1.5 f stops? I am curious to know.


with best regards,
Sury

[01af]

... would you explain how you arrived at 1.5 f-stops? I am curious to know.

It's not really 1.5 f-stops. At the same distance and the same angle of view (= equivalent focal length), the larger format needs an aperture number that is greater (= smaller aperture) by the linear form factor---i. e. 1.53× in the case of APS-C and 35-mm formats---for the same depth-of-field at small magnifications. That's just a tad more than one f-stop (1.23 f-stops, to be precise, or approx. 1 1/4 f-stops).

However, please note that same depth-of-field does not necessarily mean same degree of background blur. At the same depth-of-field, the background outside the DOF limits will appear more blurred with the larger-format camera. So if it's background blur you're interested in, rather than actual DOF, then the larger-format camera needs a smaller aperture still; better stop down by 1.5 or two f-stops. The exact f-stop for the same background blur depends on the focus distance and on the distance of the background. So at the end of the day, 1.5 f-stops for what most people will consider "the same DOF" is accurate enough for practical intents and purposes.

-- Olaf

[sury]

Thank you Sonalta for the link. Now I have a better understanding of the sensor sizes and their relative impact.
I was clear about crop factor but was so out of depth vis-a-vis DOF.

With best regards,
Sury

[David Kilpatrick]

David,
Thank you. If you don't mind, would you explain how you arrived at 1.5 f stops? I am curious to know.


with best regards,
Sury

Same calculation as Olaf, plus margin of error - the camera can not always set 1.3 or 1.23 stops. To be safe, allow 1.5 stops. If you have to use 1.33 or 1.66 or 1.5 it does not matter much either way, depends how you have the camera set up in 1/3rd or 1/2 steps.

My rule is always to go one notch beyond the exact equivalent. I also do this because we use the 24 megapixel image at a large size, and view it at 100%. Depth of field is related to final image size use. It was originally worked out for viewing a 20 x 25cm print at 45cm distance (10 x 8 at arm's length). If you view a 16 x 12/40x50cm at the same distance, you need to stop down more. So for the higher pixel count, assume you must go further than the calculation suggests.

David

[sury]

Olaf,
I was trying to find out if the relationship is linear or some other factor. I have accepted the 1.5 to 2 f stops as the equivalent but just curious if that is
emperical or if some math involved. My digital journey started with a dimage A1/A2 and to A100. As fate would have it,
I ended up getting both A900 and A700 at the same time for the price of A900. I played with A900 for about a week and felt that there is something missing
in my own knowledge that is preventing me to get the best out of a FF camera. Hence the query. I am not particular about the precision of the calculation as much
as the calculation itself. Thank you for the explanation. I am better aware of the underlying principles than before.

with best regards,
Sury

[sury]

David,
Based on your reply and Olaf's explanation, I will adopt 1.5 to 2 fstops as a rule of thumb. I am beginning to infer
that A900 is a better tool for bright light (whether natural or artificial) applications and A700 is better for available
light. May be my A2 is even better for indoor (museums etc).
Hopefully setting my expectations for the camera would lead to lesser disappointments. I am trying to understand
these complex albeit easy to use tools/instruments.
I don't mean to imply A900 cannot be used in lowlight or available light conditions any less than A700's ability in the bright light.

Wishing everyone on the forum a Happy New Year.

with best regards,
Sury

[01af]

I was trying to find out if the relationship is linear or some other factor. I have accepted the 1.5 to 2 f stops as the equivalent but just curious if that is emperical or if some math involved.

Sure there is math involved; you can compute everything to any arbitrary number behind the decimal point ... whether it makes sense or not. The relationship between small-format DOF and large-format DOF is virtually linear at small magnifications (i. e. long focus distance) and becomes increasingly non-linear at higher magnifications (i. e. close-up and macro distance).

The rule of thumb for the larger-format camera's aperture number is, multiply the smaller-format camera's aperture number with the crop factor, then round up to the next aperture number that you can actually select.

The (almost) exact formula for the degree of blur of a point in object space is here:

z = p * (f / k) * |B(f, d) - B(f, do)| / (B(f, d) + (p - 1) * f)

where

z = diameter of the circle of confusion (i. e. degree of blur)
p = exit-to-entry pupil ratio, or pupil magnification (if unknown then assume p = 1)
f = focal length
k = aperture number
d = distance (from image plane) of the point in object space to compute z for
do = focus distance the lens is set to

and B(f, d) is the function that computes the image distance b for focal length f and focus distance d; it is defined as follows:

b = B(f, d) = d/2 - sqrt(d * (d/4 - f)) for magnification m < 1
b = B(f, d) = d/2 for magnification m = 1
b = B(f, d) = d/2 + sqrt(d * (d/4 - f)) for magnification m > 1

Please note that these formulas still aren't perfectly accurate as they neglect both the distance of the lens' principal planes and diffraction effects. If you happen to know your lens' principal planes' distance then subtract that from d and do before entering these parameters into the formulas.

Also note that these formulas won't help you in any way to make better photos. But you asked ...

-- Olaf


EDIT: Removed a surplus left parenthesis from the first formula.

[sury]

Olaf,
Yes, I asked and I did get it.
Now the eternal question is: what helps me to take a better photo?
I know one answer is to go out take the pictures and have fun. What else?

Also note that these formulas won't help you in any way to make better photos. But you asked ...

-- Olaf

[jcoffin]

Olaf,
Yes, I asked and I did get it.
Now the eternal question is: what helps me to take a better photo?
I know one answer is to go out take the pictures and have fun. What else?

DoF preview is helpful, but be aware that while it gives some idea of how much DoF you'll have in the final picture, it's NOT (with most viewfinder screens) very accurate -- you need to practice a bit and compare its view with results to know how to interpret what it shows you. Of course, if you have LiveView, the rendition is much more accurate.

The big thing is to pay close attention to what you see in the viewfinder -- people tend to look at the part of the picture they're interested in, and ignore the rest. When they look at the result, (and especially when others look at the result) the rest is much more apparent, and you start to notice things like how distracting the background is, things that look like they're "growing" out of people's heads and such, etc. One of your primary jobs as a photographer is to pay enough attention to see these kinds of things ahead of time, and find angles where they don't produce problems (or, better still, finding a background that really helps the picture, not just one that doesn't hurt it).

[sury]

That is a very good point to remember especially when I tend to shoot first and review later. More than once I felt I could have gotten
a better shot if only I paid attention to the rest of the frame in addition to the part I am interested. Often I am so concerned about missing
the shot(s) that I forget to do it. I should start using DoF button. Thanks for the reminder and reinforcement.

With best regards,
Sury


[/quote]

DoF preview is helpful, but be aware that while it gives some idea of how much DoF you'll have in the final picture, it's NOT (with most viewfinder screens) very accurate -- you need to practice a bit and compare its view with results to know how to interpret what it shows you. Of course, if you have LiveView, the rendition is much more accurate.

The big thing is to pay close attention to what you see in the viewfinder -- people tend to look at the part of the picture they're interested in, and ignore the rest. When they look at the result, (and especially when others look at the result) the rest is much more apparent, and you start to notice things like how distracting the background is, things that look like they're "growing" out of people's heads and such, etc. One of your primary jobs as a photographer is to pay enough attention to see these kinds of things ahead of time, and find angles where they don't produce problems (or, better still, finding a background that really helps the picture, not just one that doesn't hurt it).[/quote]