# DoF - The Merklinger Method

16 views

### dan

Feb 11, 2002, 12:20:08 AM2/11/02
to
Harold M. Merklinger has done some interesting writing about DoF.

Basically he throws out the 'standard' hyperfocal way
and just focuses on infinity
using object size to determine the f/stop.

I'm wondering if anyone uses the Merklinger method on a regular basis?

This site has a download for calculating and printing circular DoF
charts using the hyperfocal method - useful when reading about the
Merklinger method.
http://dfleming.ameranet.com

May the Light be with you.Â©
-----
dan

### Bob Hickey

Feb 11, 2002, 7:36:55 AM2/11/02
to
I don't see the problem in the first place. I shoot all
winter, and when my eyes start to white-out or tear, I use hyperfocal
distance. Added to that, I almost always have either a red or pol. or
both on and can't see anyway. Focusing with Inf. at the far distance
causes the loss of fore ground focus. His method only forces the use of
a smaller stop than is otherwise necessary. My Rolleis don't do well
past F11, so I wouldn't use that at all.
Bob Hickey

http://photos.yahoo.com/rollei711

### Rick

Feb 11, 2002, 9:31:26 AM2/11/02
to
I've never understood all this DOF stuff...why not just focus on what you
want to focus on? If you want more DOF, just close down your apeture more.

Anyone else identify with the above remarks? Is the DOF stuff for people
with rangefinders, or am I the only one who uses the viewfinder on a camera
to *see* what I'm shooting at and how it's going to look?

"dan" <eos1...@hotmail.com> wrote in message

### Bill Tuthill

Feb 11, 2002, 12:08:26 PM2/11/02
to
dan <eos1...@hotmail.com> wrote:
>
> Basically he throws out the 'standard' hyperfocal way
> and just focuses on infinity
> using object size to determine the f/stop.
>
> I'm wondering if anyone uses the Merklinger method on a regular basis?

Not exactly. I do agree with him that results are better overall if you
focus further away rather than closer, in many cases. Autofocus systems
generally pick the AF sensor closest to the camera. Often it's better to
select a sensor that's further away, for the reasons Merklinger states.

Feb 11, 2002, 2:16:31 PM2/11/02
to
It sounds to me as if he is using the wrong dof charts --- I would consider
most dof charts to be the wrong ones anyway. FWIW I don't consider
hyperfocal focusing to be worth anything on lenses longer than 100mm max.
Where it really works is on wide angles like my 24 - for one thing anything
at a distance is too small to make out well even in a large print. Where I
have something important and large at infinity I will usually focus to
favour it - ie focus at infinity, then turn the ring to the hyperfocal
distance for say f5.6 while shooting at f11. But I use the dof preview, and
I also shoot a couple focused at infinity.

--
The Camera-ist's Manifesto
a Radical approach to photography.
A few pictures are available at
http://www.homeusers.prestel.co.uk/magor/tony

"dan" <eos1...@hotmail.com> wrote in message

Feb 11, 2002, 2:10:05 PM2/11/02
to
If you don't use the dof preview you are not "seeing" how it's going to
look. If you are...... never mind.

--
The Camera-ist's Manifesto
a Radical approach to photography.
A few pictures are available at
http://www.homeusers.prestel.co.uk/magor/tony

"Rick" <ri...@viacom.net> wrote in message news:2BQ98.189\$95.38596@news...

### Rick

Feb 11, 2002, 3:58:04 PM2/11/02
to
That's what I mean...I just preview if I need to, then take the shot.
Charts, schmarts!

"Tony Spadaro" <tspa...@ncmaps.rr.com> wrote in message
news:hGU98.87268\$A51.37...@typhoon.southeast.rr.com...

### Jerry Thomas

Feb 11, 2002, 4:03:37 PM2/11/02
to
I used to take a lot of action shots back when the Minolta SRT 101 was a
new camera. Sports mostly for my high school news paper. I made good
advantage of hyerfocal back then. It was simple really. You just picked
a stop like f/8 or f/11 and set infinity on the f stop mark then took
notice of how close the subject could be and still be in focus and just
shoot away. At that time, I used a 58mm and did my zooming / composing
in the dark room. If you just set on infinity you loose a lot on the
close in side. Using a 58 mm instead of zooming in I would see things in
the negatives that I had not noticed when I was shooting. Like an opposing
team defense holding on to a face shield.

--
Those who value safety say freedom is worthless if you're not alive to
enjoy it. Those who value freedom say life is worthless if you're not free
to enjoy it.

### Josh Osborne

Feb 11, 2002, 6:46:44 PM2/11/02
to
In article <wfW98.239\$95.48736@news>, Rick <ri...@viacom.net> wrote:
>That's what I mean...I just preview if I need to, then take the shot.
>Charts, schmarts! [...]

Right but not all SLRs let you preview.
--
Not speaking for much of anyone.
Yes my mail address really does have all that crap in it.

### David Kieltyka

Feb 11, 2002, 8:42:52 PM2/11/02
to
Rick <ri...@viacom.net> wrote:

> I've never understood all this DOF stuff...why not just focus on
> what you want to focus on? If you want more DOF, just close
> down your apeture more.
>
> Anyone else identify with the above remarks? Is the DOF stuff
> for people with rangefinders, or am I the only one who uses the
> viewfinder on a camera to *see* what I'm shooting at and how
> it's going to look?

Let's say you want to take a photo of wildflowers in a meadow along with an
interesting rock formation in the background. You want both the flowers and
the rocks to be in acceptable focus. You're using a 24mm lens and the
closest flower you want in focus is 18" away. Which aperture will you use
and at what distance will you focus to make sure everything you want sharp
is sharp?

One way is to use your camera's DOF preview. But at real small apertures, as
needed for the example above, it's hard to see much of anything through an
SLR viewfinder, much less accurately determine focus and sharpness. An
easier & faster way IMO is to use the DOF scale on your lens and the
hyperfocal focusing method.

I agree with Tony that hyperfocal focusing is useful mainly with wide angle
lenses. I almost always use it with lenses wider than 35mm.

-Dave-

### Michael K. Davis

Mar 22, 2002, 9:45:19 AM3/22/02
to
Hi!

dan <eos1...@hotmail.com> wrote:
: Harold M. Merklinger has done some interesting writing about DoF.

: I just read about it tonight.

: Basically he throws out the 'standard' hyperfocal way
: and just focuses on infinity
: using object size to determine the f/stop.

How can Merklinger acknowledge the usefulness of DoF that exists on the
near side of the plane of best focus and reject the value of DoF that
resides beyond the plane of best focus?

Don't read anything Merklinger writes about DoF for rollfilm cameras.

Do read his work on view camera movements, if you do any large format
work. It's not very well written, but after you parse through all the
gibberish, you'll find his methods for determining tilt, swing, shift,
etc. are simply brilliant. You'll be setting up faster than ever before.

: I'm wondering if anyone uses the Merklinger method on a regular basis?

They are lost souls.

[snip]

Here's an article I wrote in May of 2001:

Mike's Method for High Resolution Photography
-or-
How to Focus and Choose Apertures Obsessively

Let's jump right in by looking at the equations needed to calculate the
Best Focus distance, given the focal length of your lens and the distances
to the Near and Far Sharps in the scene. The first equation solves for
Hyper, which is then used as a variable in the second equation to actually
calculate the distance at which to focus.

Hyper =
(FL/304.8*Near)+FL/(304.8*Far)-2)/(1/(304.8*Far)-1/(304.8*Near))/304.8

Best Focus = (Hyper*304.8-FL)/(Hyper/Near-1)/304.8

(Hyper and Best Focus are in feet.)

Variables:

FL: Lens Focal Length (mm)
Near: Distance to Nearest Subject (feet)
Far: Distance to Furthest Subject (feet) - Use 3000 feet for Infinity

These two equations would be daunting if you had to key them in every time
you needed them. I use a Hewlett Packard HP 48G+ programmable calculator
to do this math in the field in less than 2 minutes. It displays the last
values I used, allowing me to overtype only those I want to change before
running the equation.

I use an Opti-Logic. 400XL Laser Rangefinder (available from CSP Outdoors
at: http://www.cspoutdoors.com, for \$279.00) to measure the Near and Far
distances. The Nears are sometimes too close for the rangefinder to
measure (<12 feet) and I must switch to using either a 10-ft. tape measure
or a Digitape Sonic Tape Measure that is extremely accurate out to about
30 feet - when there's a nice planar target to return the signal. I have
also created overlays for the distance scales on my lenses using
self-adhesive labels cut-to-fit and incremented with a very fine point
pen. I indexed these labels in feet by advancing and focusing on a
broomstick that I propped at carefully measured distances from the lens,
with the camera stationary on a tripod. So, I've got several accurate
ways to measure distances and perform crosschecks.

Once I calculate the best focus distance, using the formulae above, I find
a target that is at that distance from the camera position using the laser
rangefinder - even if it is outside the intended field of view. I swing
the camera onto that object which I have found to be at the calculated
distance, focus on the target, then swing my camera back to reframe the
shot with the intended composition.

Well that's my technique for focusing roll film cameras precisely, but
what aperture will provide just enough depth of field? Stopping down
further than necessary requires slower shutter speeds than we might have
enjoyed and increases the effects of diffraction. As Circles of Confusion
shrink while stopping down, diffraction's Airy disks increase in size.
There's a point at which the two are optimized against each other -
there's no need to make the CoC's at our Near and Far Sharps any smaller
if doing so will make diffraction's spread function larger than the
maximum CoC diameter. The quest for King Depth of Field has ruined many a
shot - especially with small formats (35mm and smaller) where diffraction
kicks in at wider apertures than it does with the larger formats.

The aperture at which this happens depends on what we have selected as our
Maximum Permissible Diameter for Circles of Confusion, which, in most DoF
calculators, is treated as a constant for a given format - a huge, but
common oversight in my opinion. For example, many DoF calculators use the
value 0.03mm as the Maximum Permissible Diameter for Circles of Confusion
for all calculations done for the 35mm format. This is entirely too rigid
and I believe it's the greatest contributing factor to most people's
disappointment with DoF calculators, DoF tables and yes, the DoF scales
engraved on our lenses.

Depth of Field calculations rely not only on the desired Maximum
Permissible Circle of Confusion diameter and the focal length of the lens,
but also on the format diagonal. When we make a print by cropping, the
format diagonal is no longer that of the full frame image - why is this so
commonly overlooked in DoF calculations? DoF calculations done for full
frame will fail when cropped portions of the original image are enlarged.

I contend that the Maximum Permissible Diameter for Circles of Confusion
should not be fixed for a given format when doing DoF calculations. It
is a variable, not a constant, and this variable should itself be
calculated, taking into account all the variables that affect the
perception of Depth of Field when viewing the final print. These
variables include viewing distance (the further away you are from a print
the sharper it looks), resolving power of the human eye (generally agreed
to be about 5 lp/mm at a viewing distance of 25 cm (9.84 inches) for an
adult with healthy vision), the minimum combined resolving power of the
lens and film together as a system (seldom better than 45 lp/mm in the
corners for the best lenses and color films or about 60 lp/mm with the
best black and white films), the enlargement factor (degree of
magnification required to enlarge the negative or slide to final print
size - and this figure must also acknowledge any cropping anticipated,
unless you're quite certain that your image will be printed full frame.)

So, has the selection of an aperture just become way more complicated than
you wanted it to be? It's not so bad. First, let's look at how I select
the Maximum Permissible Diameter for Circles of Confusion:

I do it by working backward from the final print dimensions and desired
resolution in that print.

Maximum Permissible CoC Diameter =

1 / Desired Resolution at the Print / Desired Enlargement Factor

Let's say we want an extremely sharp 8x10 print from 35mm - here's how to
make it work without compromising anything by stopping down more than
necessary...

8x10 prints have a 4:5 aspect ratio, not 2:3 like the full frame 24x36mm
format of 35mm film. So, at best, we'll only be using a portion of the
24x36mm negative or slide - 24x30mm. This crop has an on-film diagonal of
only 38.42mm, vs. the original 43.27mm.

OK, how much larger is an 8x10 print than our cropped 35mm negative? The
diagonal of an 8x10-inch print in millimeters is 325.3 and the diagonal of
our cropped negative is again, 38.42mm, so we just have to divide 325.3mm
by 38.42mm to get the enlargement factor: 8.47.

Now that we have the enlargement factor, let's figure out how much
resolution we need on-film to get 5 lp/mm resolution in the final print
(this is the resolution that will survive scrutiny by healthy eyes at a
viewing distance of only 9.84 inches (25cm). (If you want your 8x10 print
to survive examination at closer viewing distances, substitute a larger
value than 5 lp/mm in the following calculations. For example, 10 lp/mm
at the print would tolerate scrutiny at a viewing distance of only 5
inches. Can you focus your eyes that closely? Can your lens and film
deliver enough resolution on-film to deliver 10 lp/mm at the print after
magnification?)

Assuming we want 5 lp/mm AFTER magnification by an enlargement factor of
8.47x, we must limit all of our on-film spread functions (CoC's and Airy
disks, for example) to 8.47 * 5 lp/mm BEFORE magnification: That's 42.35
lp/mm on-film, just within the 45 lp/mm ceiling I believe is the best that
can be achieved with today's best lenses and color films, so our 8x10
enlargement is a realistic goal.

By the way, if 45 lp/mm seems too conservative a figure for today's best
lenses and color films, consider that Fujichrome Provia 100 F's resolution
in low-contrast 1.6:1 lighting is 60 lp/mm and the aerial resolution of
the finest lenses, like those of the Mamiya 7 6x7cm rangefinder, are only
about 180 lp/mm. The formula for calculating the combined resolving power
of a lens/film system is:

1/Rtotal = 1/Rlens + 1/Rfilm

In the case of a system combining Fujichrome Provia 100 F with a Mamiya 7
lens, we get:

1/180 + 1/60 = 1/45

So, Rtotal equals 45 lp/mm. Surprise: The combined system resolution is
LESS than that of either of its components!

OK, where were we? Oh yeah... We figured out that because we want 5
lp/mm at the print after enlarging to 8x10-inches from 24x30mm, we will
need 42.35 lp/mm on-film BEFORE magnification. The system resolving power
can deliver that, so how do we make sure our chosen apertures don't create
Circles of Confusion or Airy Disks larger than this?

To convert lp/mm resolution into an equivalent spread function diameter
and vice-versa, just take the reciprocal of one to get the other. So
here, where we know we want our on-film resolution to be 42.35 lp/mm,
let's just take the reciprocal to get the Maximum Permissible Diameter for
Circles of Confusion (and diffraction's Airy Disks) on-film: 1 / 42.35 =
0.0236mm - that's quite a bit SMALLER than the 0.03mm figure so often used
in Depth of Field calculators that erroneously treat this variable as a
constant within a given format!

Going back to the formula above, in this scenario, our Maximum Permissible
Circle of Confusion is:

1 / 5 lp/mm desired at the print / 8.47 enlargement factor = 0.0236mm

Presto: We now have the maximum diameter on-film we are willing to let
any spread function reach, for our nominally cropped 35mm negative or
slide to produce an 8x10-inch print that will deliver a 5 lp/mm
resolution!: 0.0236mm.

NOW, we're ready to calculate the aperture that will give us just enough
Depth of Field to produce Circles of Confusion of THAT diameter, on-film,
without inducing visible diffraction nor suffering the slower shutter
speeds that would come with stopping down further! Cool huh?

Best F-Stop = FL^2 / (Hyper * 304.8 * CoC)

where:

Hyper is the same value calculated above for use in the Best Focus formula

FL is the focal length of your lens in mm

CoC is the Maximum Permissible Diameter for Circles of Confusion, on-film
(mm)

Note: In English, FL^2 reads "focal length squared"

Now, there's one last calculation to do - you have to make sure that this
Best f-stop doesn't induce visible diffraction. Here's the formula for
calculating the f-stop at which diffraction's Airy disks will reach the
same size as your chosen Maximum Permissible Circles of Confusion:

Diffraction F-Stop = CoC / 0.00135383

So for our 8x10 scenario, where we want 5 lp/mm in the final print, having
calculated a Maximum Permissible Diameter for CoC's of 0.0236mm, we can
calculate the f-stop at which diffraction will become visible:

0.0236 / 0.00135383 = 17.44 (or f/17.44)

This means that we simply MUST NEVER stop down below f/16 in search of
additional DoF! Doing so will cause the diameter of diffraction's Airy
disks to actually exceed our Maximum Circle of Confusion diameters (those
at the Near and Far sharps.)

The following list of f-stops is helpful in setting your aperture control
precisely - it shows the "real" f-stop values interlaced with 1/3-stop
increments:

1.0 -
1.1
1.3
1.4 -
1.6
1.8
2.0 -
2.2
2.5
2.8 -
3.2
3.6
4.0 -
4.5
5.0
5.7 -
6.3
7.1
8.0 -
9.0
10.1
11.3 -
12.7
14.3
16.0 -
18.0
20.2
22.6 -
25.4
28.5
32.0 -
35.9
40.3
45.3 -
50.8
57.0
64.0 -
71.8
80.6
90.5 -
101.6
114.0
128.0 -

I have this taped to the back of my HP48G+ so that when it spits out a
weird f-stop, I know how to index it on my lenses, in 1/3 stops.

Now let's take a look at an example of what the Best F-Stop and
Diffraction F-Stop formulae would require of us in the field:

Let's say we're using a 50mm lens on our 35mm camera and we want to make
one of these tack-sharp 5 lp/mm 8x10 prints. Remember, we can NOT use
f/22 because the f-stop at which diffraction is maximized against our
chosen CoC diameter is f/17.4 - and that's not even 1/3-stop down from
f/16, so f/16 is all the stopping down we are allowed to do - go further
and you'll degrade your print with diffraction - at least when viewed at
the target viewing distance of 9.84 inches (25cm).

How close can our Near Sharp be and still have Infinity in focus (a Far of
3000 feet)? Not very close! How about a whopping 10.85 feet! That's not
what it says on your lens' engraved Depth of Field scale is it? Nothing
comes easy - in order to shrink our CoC diameters, we've had to compress
our Depth of Field, thus pushing the distance at which our nearest
subjects may reside farther away from the camera than they would be if our
requirements were less aggressive.

With a 24mm lens, it becomes a little easier to maintain sufficient
distances from the Near: Again at f/16, the smallest aperture we can use
to avoid diffraction, a 24mm lens can deliver our chosen 0.0236mm diameter
CoC's from 2.5 feet to Infinity.

Remember these figures apply strictly to the 8x10-inch print made from a
24x30mm crop, to deliver 5 lp/mm resolution at the print, which will be
viewed at a distance of 9.84 inches or more. Change any of that and your
CoC should be recalculated for use in a recalculation of the Best F-Stop
and the Diffraction F-Stop.

Also: Do not neglect to consider whether the calculated Best F-Stop
permits a shutter speed sufficient to freeze both subject and camera
motion, if any. If not, you'll need to go to a faster film, or just
underexpose and then push process the film you have. If the calculated
Best F-Stop required for the specified Near and Far sharp distances is
smaller than you can use, for any reason, you'll have to increase the
distance between your camera and the nearest subject or decrease your
focal length without changing the distance to the Near. In either case -
it's time to recalculate!

Lastly, if you suspect you are having problems with film flatness, it can
help to recalculate everything with about a 50% increase in desired print
resolution (go for 7.5 lp/mm instead of 5 lp/mm, for example.) This will
move your Nears farther still from you camera, but if that's what it
takes, do it.

That's all of it in a nutshell. Grab your programmable calculator or
spreadsheet and have at it. I can forward specific instructions for
programming these formulae (and others) to anyone interested in using an
HP 48G+ to do this math quickly, in the field.

If you have access to Microsoft Excel, have a look at these two

MDoF993s.xls and CoCCal21.xls

These (or later versions) can both be found at
http://briefcase.yahoo.com/zilch0md in the Tools folder.

MdoF993s.xls will help you choose a maximum permissible CoC diameter and
then allow you to print DoF tables for use in the film. It assumes a
desired print viewing distance of 10-inches.

CoCCal21.xls assumes you have some other method of calculating DoF or
making DoF tables, but guides you in selecting a maximum permissible CoC
diameter, for any combination of system resolution, anticipated viewing
distance, desired print resolution and enlargement factor - all the stuff
that's so often ignored in discussions of DoF and at the very core of why
there's so much disillusion about formulas that are actually very reliable
and very practical.

Mike Davis

--

### Gary Frost

Mar 22, 2002, 2:05:27 PM3/22/02
to
Nice article on the subject Michael. I have both of Merklinger's books.
I agree with you here on the lunacy of his 'throwing out' the
usable DOF beyond infinity. Much better to just use a smaller CoC,
and still use hyperfocal. Also, what part of the field is in sharpest
focus, infinity or close-up, is a choice to make with each photo.

I find all of this 'armchair/rainy day' photography though and not much
practical use in the field. For 35mm, using a calculator, measures, tables
destroys the speed advantage of the format. For large format, it is
already slow enough without adding the complicated steps Merklinger
proposes!

Well, I have a problem using a calculator in the field so consider
my viewpoint with that in mind.

For 35mm, the DOF scale on the lens still works for me after you determine
what CoC was used. According to your example below, my 50mm Nikkor
is about 1/2 stop shy of your requirement. (.3 CoC instead of .25?)
Sorry about all those lenses without a DOF scale, I don't have any ;^)
(also, with longer focal lengths they become unusable)
Maybe carry a table around for a while until you get to know the FL.

For large format and Merklinger's method of determining tilt in the field,
I think it would quickly become the slowest and most cumbersome step
in the process of taking a picture. His Chapter 5 Example of how to
apply his method is...well an _example_ .
First you must determine his 'J' distance with reasonable accuracy.
In his example it is 8 feet. In practical field situations it will range
from that out to 50-60 feet, under the ground beneath the camera.
Just how does one figure out what that distance is? Survey equipment?

In step 2 he looks up the tilt angle And sets this on the front standard
with a protractor! ( most fields don't have an angle scale)
...then he focuses on the ground glass _ONLY_ for the far distance,
not checking the near, to verify the tilt is correct. (this would take
maybe 3-5 seconds) To me, (and many others), this is sheer lunacy.

What is a better alternative? After selecting the ideal plane of sharp
focus. ( Merklinger can help in this step, but you don't need the
tables and measurement to do it) Adjust the tilt as it has been done for
100 years: using a loupe on the ground glass. Still the most accurate
and fastest method. This can be completed before you can even think about
what 'J' might be and reaching for his table of tilt angles.
There are some clever simple methods to determine DOF and f/stops as well,
but all this is already too far off topic for the NG.

After blasting his field methods let me also say that I highly recommend
his book on focusing the view camera. It is an excellent reference text on
the subject I have never seen treated in such detail anywhere else.
There is valuable knowledge to take and use in the field. But I leave
the book, tables, and calculator at home.
Gary Frost

### Gary Frost

Mar 22, 2002, 2:36:10 PM3/22/02
to
ooops....thats 0.03 and 0.025 on the size CoC....obviously

### David Littlewood

Mar 23, 2002, 2:48:52 PM3/23/02
to
In article <10168083...@nnrp2.phx1.gblx.net>, Michael K. Davis
<zil...@primenet.com> writes

>
>Here's an article I wrote in May of 2001:

...Which is very good. I have a couple of comments, in line below.
>
[snip]

>
>Well that's my technique for focusing roll film cameras precisely, but
>what aperture will provide just enough depth of field? Stopping down
>further than necessary requires slower shutter speeds than we might have
>enjoyed and increases the effects of diffraction. As Circles of Confusion
>shrink while stopping down, diffraction's Airy disks increase in size.
>There's a point at which the two are optimized against each other -
>there's no need to make the CoC's at our Near and Far Sharps any smaller
>if doing so will make diffraction's spread function larger than the
>maximum CoC diameter. The quest for King Depth of Field has ruined many a
>shot - especially with small formats (35mm and smaller) where diffraction
>kicks in at wider apertures than it does with the larger formats.

I have always found this, empirically, but have been criticised before
for saying it - by people pointing out that the formula for the size of
the Airy disc includes the f-number as a variable, not the physical size
of the aperture. Do you reach this conclusion based solely on the fact
that LF photos are generally enlarged by a smaller factor, or do you
have something else in mind?

I feel 5 lp/mm is a little optimistic, and prefer 10. This may be
because my normal print size is 12x16, but I still want it to reveal
detail from 10 inches away. I note that Ctein suggests 30 lp/mm for the
very best quality work (and he is still referring to the finished print
here) but I think that may be too perfectionist. Anyway, it is simply
not achievable in 35mm work.

I believe this formula should be 1/R^2 = 1/Rlens^2 + 1/Rfilm^2 +
1/R(other factor)^2

The last bit is just to demonstrate that every factor in the chain comes
in - enlarger lens, focus error, paper sharpness etc. - there may in
reality be 5 or 6 factors in the equation, though some will have a
minimal effect.

>
>In the case of a system combining Fujichrome Provia 100 F with a Mamiya 7
>lens, we get:
>
>1/180 + 1/60 = 1/45

Whereas my formula gives 1/56.9 - say 1/57. I think this is correct; all
factors affecting resolution will affect the overall figure, but only
those reasonably close to the "worst" factor will have a large impact.

This seems to equate to Resolution = 750/f-stop. I believe the
approximation should be R = 1500/f-stop (for green light) where f-stop
includes a magnification factor (i.e. for resolution on film which will
be enlarged 10x, the f-stop is lens f-stop times 10).

>
>So for our 8x10 scenario, where we want 5 lp/mm in the final print, having
>calculated a Maximum Permissible Diameter for CoC's of 0.0236mm, we can
>calculate the f-stop at which diffraction will become visible:
>
>0.0236 / 0.00135383 = 17.44 (or f/17.44)
>
>This means that we simply MUST NEVER stop down below f/16 in search of
>additional DoF! Doing so will cause the diameter of diffraction's Airy
>disks to actually exceed our Maximum Circle of Confusion diameters (those
>at the Near and Far sharps.)

I would actually arrive at the same conclusion, but by using 10 lp/mm
and 1500/effective aperture; thus:

1500/160 = (approx)10

Where the effective aperture = lens aperture (f/16) times
enlargement factor (10).
>
[snip]

>
>Lastly, if you suspect you are having problems with film flatness, it can
>help to recalculate everything with about a 50% increase in desired print
>resolution (go for 7.5 lp/mm instead of 5 lp/mm, for example.) This will
>move your Nears farther still from you camera, but if that's what it
>takes, do it.
>

As above, this can be taken into account in the 1/R^2 = formula above,
though your approach is probably a good estimate.

[snip]
--
David Littlewood

### Michael K. Davis

Apr 6, 2002, 10:17:58 PM4/6/02
to
Hi!

David Littlewood <da...@nospam.demon.co.uk> wrote:
: In article <10168083...@nnrp2.phx1.gblx.net>, Michael K. Davis

: <zil...@primenet.com> writes
: >
: >Here's an article I wrote in May of 2001:

: ...Which is very good. I have a couple of comments, in line below.
: >
: [snip]
: >
: >Well that's my technique for focusing roll film cameras precisely, but
: >what aperture will provide just enough depth of field? Stopping down
: >further than necessary requires slower shutter speeds than we might have
: >enjoyed and increases the effects of diffraction. As Circles of Confusion
: >shrink while stopping down, diffraction's Airy disks increase in size.
: >There's a point at which the two are optimized against each other -
: >there's no need to make the CoC's at our Near and Far Sharps any smaller
: >if doing so will make diffraction's spread function larger than the
: >maximum CoC diameter. The quest for King Depth of Field has ruined many a
: >shot - especially with small formats (35mm and smaller) where diffraction
: >kicks in at wider apertures than it does with the larger formats.

: I have always found this, empirically, but have been criticised before
: for saying it - by people pointing out that the formula for the size of
: the Airy disc includes the f-number as a variable, not the physical size
: of the aperture. Do you reach this conclusion based solely on the fact
: that LF photos are generally enlarged by a smaller factor, or do you
: have something else in mind?

First, let me clarify/restate what I said above: The quest for King Depth

of Field has ruined many a shot - especially with small formats (35mm and

smaller) where diffraction kicks in at lesser f-Numbers than it does with
the larger formats. In other words, it is because f/22 is a physically
smaller diameter of aperture for a 50mm lens (for 35mm format) that we end
up with larger Airy disks on-film than we would with a 4x5 camera's 200mm
lens at f/22 (200mm being an equivalent focal length.) So the 200mm lens
at f/22 will produce smaller Airy disks on-film. Now consider the lesser
degree of enlargement necessary to make a print of a given size and you
can see we have another isssue.

: >
: >The aperture at which this happens depends on what we have selected as our

I like 7.5 lp/mm actually. I find that's enough for what I do, but could
see shooting for 10 lp/mm if I was working with any of the infamous
120 rollfilm holders made for view cameras - which have serious film
flatness problems - or with any sheet film larger than 4x5.

: >
: >So, has the selection of an aperture just become way more complicated than

I didn't want to go that deep - I was just trying to show that 45 lp/mm
isn't excessively conservative - but yes, we could sum the reciprocals
of several "other factors". Regarding whether or not to square the
denominators. I've seen it both ways. I find the whole exercise somewhat
moot since I am very confident from empirical observation that 45 lp/mm is
about all I can hope for in the corners, from great lenses with a color
film like Provia 100F.

: The last bit is just to demonstrate that every factor in the chain comes

That's true, since the CoC diameter is the reciprocal of desired
resolution.

: I believe the

: approximation should be R = 1500/f-stop (for green light) where f-stop
: includes a magnification factor (i.e. for resolution on film which will
: be enlarged 10x, the f-stop is lens f-stop times 10).

The reciprocal of 1500/f-stop would give us the radius of an Airy disk,
not the diameter. I have chosen to stop down until the DIAMETER of an
Airy disk has reached my chosen CoC diameter.

If I used 1500/f-stop, I would have to change my formula to

Diffraction F-Stop = CoC / 0.00270766

Which would have me working at f-stops that are two stops wider (larger
aperture) than my formula mandates (f/11 instead of f/22 for a chosen CoC
diameter of 0.03 for example). No thanks.

: >
: >So for our 8x10 scenario, where we want 5 lp/mm in the final print, having

: >calculated a Maximum Permissible Diameter for CoC's of 0.0236mm, we can
: >calculate the f-stop at which diffraction will become visible:
: >
: >0.0236 / 0.00135383 = 17.44 (or f/17.44)
: >
: >This means that we simply MUST NEVER stop down below f/16 in search of
: >additional DoF! Doing so will cause the diameter of diffraction's Airy
: >disks to actually exceed our Maximum Circle of Confusion diameters (those
: >at the Near and Far sharps.)

: I would actually arrive at the same conclusion, but by using 10 lp/mm
: and 1500/effective aperture; thus:

: 1500/160 = (approx)10

: Where the effective aperture = lens aperture (f/16) times
: enlargement factor (10).
: >
: [snip]
: >
: >Lastly, if you suspect you are having problems with film flatness, it can
: >help to recalculate everything with about a 50% increase in desired print
: >resolution (go for 7.5 lp/mm instead of 5 lp/mm, for example.) This will
: >move your Nears farther still from you camera, but if that's what it
: >takes, do it.
: >
: As above, this can be taken into account in the 1/R^2 = formula above,
: though your approach is probably a good estimate.

Thanks!

Mike

: [snip]
: --
: David Littlewood

--

### Michael K. Davis

Apr 6, 2002, 10:24:40 PM4/6/02
to
Just wanted to give you the source of the formula I use:

See the following text at:

http://www.photo.net/learn/optics/lensTutorial

***
If, for simplicity, we take 555 nm as the wavelength, the diameter of
the [Airy disk's] first zero, in mm, comes out to be 0.00135383 N. As was
mentioned above, the normally accepted circle of confusion for depth of
field is .03 mm, but .03/0.00135383 = 22.1594, so we can see that at f/22
the diameter of the first zero of the diffraction pattern is as large is
the acceptable circle of confusion.
***

Thanks,

Mike
--