Depth of Field, Angle & Field of View, & Equivalent Lens Calculator

Camera and Lens

Basic DoF Functions


Enter a crop factor (eg. "6.7" or "0.25") or dimensions in mm as width x height (eg. 36x24 or 15.2 x 9.5). See notes section for details.
mm
f/

Extended Functions (Click to Show)

See notes on extended functionality.

A resolution in MP (eg. "24MP" or "24 MP"), or in pixels (eg. 6000x4000 or 6000 x 4000).

Shutter speed in fractional (eg. 1/500) or decimal notation.

Equivalent Lenses

Format Focal Length Av Setting* F-number
Results go here.

* The Av setting is the camera aperture setting, in 1/3rd-stops, that will closely approximate source
lens's depth of field. Available values range from f/1 to f/64 in 1/3rd stops.

For the supported formats it will calculate the hyperfocal distance, near and far depth of field and total available depth of field for the lens specified. As well as the equivalent lens and aperture required to get approximately the same composition and depth of field in one of the other supported formats.

Note: The experimental values and extended functions are part of an ongoing experimental concept that I’m currently developing. Please don’t contact me and ask me what it is or how to interpret it. It is only included and displayed so I can move forward on developing an idea.

Custom Frame Sizes

As of April 2016, the calculator now supports custom frame sizes. These can be entered as either a crop factor or as the dimensions, in mm, of the frame to be used.

For crop factors, the reference frame is the 3:2 aspect ratio 135-format (i.e. 36 x  24 mm) film frame. Cropped frames will retain the 3:2 aspect ratio. Crop factors are crop of the reference frame, therefore a value larger than 1 will produce a smaller frame. Entering a value smaller than 1, e.g. 0.5, will generate a frame larger than the reference frame.

The second option is to enter the dimensions of the frame in mm. This should be entered in the format of “width x height”, or “dimension_1 x dimension_2”. Whether the width precedes the height or vice versa will only change the horizontal and vertical values presented in the angle and field of view sections. Spaces between the numbers and the ‘x’ are ignored. Decimal values are accepted.

Depth of Field Graph

The depth of field graph presents depth of field curves for 8 full-stop aperture settings from f/1.4 to f/16. This is done using the current frame size, custom circle of confusion, and focal length as specified in the Basic DoF Functions settings area.

A couple of points to note about the graph it self. Curves that stop abruptly after steeply curving up have exceeded the 10 meter DoF limit I’ve imposed on the graph. Beyond this point (at least the next iteration of the computation) the DoF will have effectively gone to infinity.

The distance range is also limited artificially. The closest distance that is computed is 4 times the focal length. The furthest distance is computed relative to focal length with wide-angle lenses being allowed to calculate out relatively further than telephoto lenses. This is to prevent the chart from becoming unnecessarily unwieldy; where super-telephoto lenses are being calculated out to 1000s of feet/meters when typically you’ll use them at considerably closer distances..

The chart can be fine-tuned in two ways. First, the slider along the bottom controls the range of distances. Moving the two handles closer to each other will narrow the distance range similarly. Secondly, the lines for various apertures can be toggled on and off by clicking their respective legend box.

Finally, you can save the chart image by right clicking on it and selecting “Save image as…” or the equivalent in your browser.

Methodology

DOF and hyperfocal distances are calculated using the following formulas.

Where:
  • H is the hyperfocal distance
  • f is the focal length
  • s is the focus distance
  • Dn is the near DoF limit
  • Df is the far DoF limit
  • N is the f-number
  • c is the circle of confusion

Equivalent lenses are calculated so that the focal length produces the same approximate angle of view and the f-stop results in an aperture diameter equal to the base lens’s aperture diameter which will produce the same depth of field.

Update History

2017-07-18: Added panorama shift increments to the calculator. Pano shift increments target a 35% overlap of the previous frame rounded to the nearest 2.5° increment, and then shows the actual overlap that will occur with that setting. To be used to calculate the rotation of a panning base divided in 2.5° increments, such as the base on a Really Right Stuff tripod head or PC-LR/PRO panning clamp.

2017-05-18: Added DoF at aperture chart. Chart displays the depth of field for various aperture (f/1.4-11 in full stop increments) from 4x the focal length to a reasonably long focus distance ( dmax ~= focalLength * ( 750 * focallength / log(focalLength) ) ). Lines that stop abruptly when curving up would have gone to infinity by the next iteration.

2017-05-17: Added ability to specify custom circle of confusion under the extended functions area (click where it says click to show extended functions).

2017-05-16: There are lots of changes with this release, some may result in subtle differences with other online calculators and previous versions of this calculator.

  • Crop factors are now calculated on the fly using the diagonal of the format (including custom formats). I am not using the standard approximations (i.e. 1.6x for Canon APS-C).
    • Crop factors are shown as a crop of 135-format (36×24 mm) film. Values larger than 1 are frames smaller than “full frame”, values smaller than one are frames larger than “full frame”.
    • Circles of confusion are calculated as the crop factor ratio of 0.029 (135-format). As a result the new crop factor calculations may result in slightly different CoCs than other calculators.
  • Changed precision of displayed output values.
    • Metric results are rounded to 3 significant figures, pursuant to the least accurate measures used in the computations.
    • Imperial (feet, inches) are rounded to show a reasonable level of precision. Errors are kept at or below 0.1%. Above 1000 inches, values are shown as decimal feet. Above 10,000 inches, values are shown as whole feet only.
  • Changed URI hash-fragment format to JSON based format to allow for easier extensible (bookmarks using the old format will still work).
  • Reorganized the format list to group formats by typical use.
  • Added new formats, specifically video formats including; Canon’s 5D mark IV and 1DX 4K crop factors, Red’s Epic/Weapon, and Arri’s 65mm format.

2017-05-08: Fixed bug where custom aperture wouldn’t clear when switching back to the standard selections. Reformatted table to support rendering on mobile devices and other devices with small screens. Added more extended experimental functionality, including calculating camera/subject motion for 100% pixel sharpness and acceptable print sharpness.

2017-03-13: You can now enter a custom aperture value that isn’t in the standard apertures list. There is currently an outstanding bug on with this in that it doesn’t persist correctly through the URL hash (# at the end). However, the calculations using it are done correctly.

Also I’ve reduced the precision of the stored aperture values, so some results may be slightly different form previous versions.

2016-04-01: Updated to allow the use of a custom frame size or crop factor. Enter the custom frame size or crop factor in the “Custom frame size box”.

You can enter a frame size in mm as width x height (eg. 24 x 12), decimals are permitted. Don’t specify the “mm”, and spaces around the x are ignored. The crop factor is calculated internally as the diagonal as referenced to the diagonal of a 35mm (36×24) frame.

You can enter a custom crop factor as a decimal number. Numbers >1 (e.g. 1.5) result in a frame that’s smaller than 35mm. Numbers <1 (e.g. 0.5) result in a frame that’s larger than 35mm. In this mode the aspect ratio of the frame is assumed to be 3:2. If you want a different aspect ratio frame, you’ll need to specify the dimensions directly.

2014-05-13: Updated script to use the same engine used by tools.pointsinfocus.com/dofcalculator and to store current settings in the URI to allow linking to a specific setup.

2014-02-05: Added 1/1.7″ CCD used in many compact cameras and the Pentax Q mirrorless cameras.

2014-02-03: Clicking on the format in the equivalent lens chart will update the lens setting to match that format as closely as the calculator allows.

2014-01-28: Added angle and field of view calculations. Angle and field of view are show for the selected format (i.e. 35mm or APC-S) and may not reflect the exact angle or field of view for the equivalent lens if the platforms aspect ratio is different.

2014-01-12: Added support for metric distance input and output formatting. And support for preset focus distances roughly corresponding to various types of portraits.

2011-01-17: I’ve added some features to make computing AF calibration data easier. The first is the AF Test Dist button that sets the focus distance to the minimum recommended AF test distance of 50 times the focal length. The second is the addition of a 1/8th DoF measure to the outputs.

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Comments

tex andrews

Please add Pentax 645D/Z

Jason Franke | admin

@tex andrews,

That’s a reasonable request, I’ve added the format under 645D/IQ250/H5D-50c. You might need to force reload the page (shift+f5 or shift+ctrl+r/shift+command+r) for it to show up.

Gabe

A custom sensor size or multiplication factor would save you from having to add more formats. This is a great calculator, but I came here hoping to find common CCD calculations. 1/3.2″ for iphone S5, 1/4″, 1/6″, 1/8″, 1/10″ CCDs common on lesser cell phones as well as security cameras.
Regardless, thanks for the nice page.

Jason Franke | admin

Gabe,

That’s actually a good idea, I’ll have to look into implementing that.

Nameless Person

Could you add 5×7 as you got 4×5 & 8×10…?

Jason Franke | admin

That’s easy enough, I’ve also added super 8mm and super 16mm film since there seems to be some movement in those formats (Black magic’s pocket cine camera and the new Kodak film camera).

Nameless Person

Nice, thanks. I use this a lot!

Andrew Batson

Question. I have a 60D with an APS-C (1.62x) sensor. So I choose that in the drop down above. On the 60D you can either attach a lens that is EF (full frame – used commonly with a 5D), in which the 1.62 crop is inherently applied to the focal length. OR you can attach an EF-S lens (same mount but opening tailored for the smaller sensor) which holds the focal length true for the APS-C sensor.
When inputing the focal length above for a EF Full frame lens attached to the APS-C sensor, I have do the 1.62x calculation first, correct? i.e. an EF 30mm would be effectively a 48.6mm on the APS-C sensor. I should input 48.6mm in the focal length section above? Correct?

Jason Franke | admin

Hi Andrew,

Thanks for the question.

The short answer is that you always enter the actual focal length that’s printed on the lens.

The long answer is a bit more detailed but it’s worth going over at least quickly.

Focal length is a measure of how strongly a lens bends or focuses light. A lens’ focal length doesn’t care about the sensor behind it at all, it’s a property of the lens and only the lens. The same focal length will have different angles of view if you put a different sensor or frame size behind it, but the lens focuses/bends light the same way (it’s a bit more complicated than this in reality, but that gets into a lot more optical engineering than I want to go into here).

For example, a 50mm lens on your APS-C camera has a an angle of view that would commonly be described as being “short telephoto”. A lens with the same focal length on a full frame camera, would be described as having a “normal” field of view. And finally a 50mm lens on a medium format camera would best be described as having a “wide angle” view. All of these lenses fundamentally “bend light” the same way, but because the frame gets bigger the angle of view increases too (the edges are further and further away so the same amount of bend results in light coming form wider and wider angle to match).

Photographers complicate the matter because they often say focal length when what they’re really talking about is angle of view (and given that it’s much easier to say 35mm than 74 degrees 10 minutes it’s no wonder why). This is what is being talked about when you do the “equivalent focal length” dance where you multiply or divide by the crop factor.

However, the focal length, being a property solely of the lens does not change when you change the size of the sensor; the angle of view does, but not the focal length.

This calculator uses the actual focal length of the lens, not the “equivalent angle of view focal length” that photographers talk about when comparing things. So there’s no need to do anything to focal length, just use the number that you had the lens set to.

Also, to clarify a point. EF-S lenses do not “hold the focal length true” for APS-C cameras. The focal lengths of those lenses (as printed on them) are the real focal lengths of the lens, and would be the same as the focal length as on an EF lens. That’s why they have different focal lengths than full frame counter parts for the same approximate angles of view.

EF-S lenses specifically do 3 things:

  • They provide angle of view ranges that match traditionally defined and useful ranges (i.e. wide to short-telephoto, or ultra-wide to wide angle), by using different focal lengths as required by the smaller sensor. (This can be generalized to all crop lenses, like Nikon’s DX or 3rd party crop lenses.
  • They have a shorter back focus distance, which allows the rear element to be placed closer to the sensor; the practical implication of this is that they can’t be mounted on a full frame camera (3rd party, e.g. Sigma, crop lenses are not EF-S, they use EF mounts), but this offers Canon benefits in designing the lenses (they don’t have to be as strongly of a retro-focal design).
  • They have a smaller image circle that won’t fully cover, or do so with good quality in the corners, a full frame sensor (again this is an engineering trade off as it allows some aspects of the lens to be made smaller.

Also the equivalence dance applies the same to them as it does to EF lenses. An EF-S 17-85mm zoom is the crop body equivalent to the EF 28-135mm zoom for full frame cameras. If you were going to jump to full frame, you’d want to multiply all your lenses’ focal lengths by the crop factor to figure out what focal lengths you want for full frame lenses to give you the same coverage.

I know that’s probably a lot more than you were bargaining for, but I hope that answers your question and clears up some possible misconceptions.

Frank

Thank you for posting this valuable tool – I have one question:
How do you calculate the distances for the different test situations (Headshot, Head & Shoulders, etc.) – I naively assumed that here the corresponding distance is based on an equal Field of View (e.g. Diagonal), however, I find different values for Field of View with different focal lengths (equal sensor size). Where is my mistake?
Best regards, Frank

Jason Franke | admin

@Frank,

Nope, that’s not your error at all. I was improperly simplifying the trig that handled calculating the distances on the assumption that the error wouldn’t matter that much for the intended use. I’ve corrected that to use the proper formulas.

For the record, I use the horizontal (long axis) of the for the distance approximations, since that’s how I expect those kinds of images would be shot (i.e. as portraits). The AF test distance is just 50 times the focal length which is what was recommended by Canon and Nikon in their literature in the past. Other than the AF test distance preset, the intent of the distance buttons is to create an approximate distance number, not to be an exact standard.

Thanks for taking the time to check things.

Frank

Dear Jason,
thank you for the very rapid answer and the correction. However, I am still somewhat puzzled:

E.g., in the tool the “Head&Shoulder” preset for Canon APS-C gives out a horizontal FOV of 30 cm @ 20 cm distance for 15 mm FL, but 68 cm HFOV @ 307 cm distance for 100 mm FL. Is that big variation in HFOV (30 cm to 68 cm) intended ?

If you would calculate the WD (working distance in mm) from the angle of FOV (AFOV(°)) as

WD (mm) = HFOV (mm) / (2x tan(AFOV(°)/2))

and AFOV(°) from the height (h) of the sensor in mm and the focal length (fl) in mm as

AFOV(°) = 2 x arctan (h/2fl)

you could preset HFOV as e.g. 500 mm (for head&shoulders) and would receive the following combinations:

34 cm distance @ 15 mm FL
227 cm distance @ 100 mm FL

Is that correct?

Best regards, Frank

Jason Franke | admin

@Frank,

The distance presets should be working correctly now. More buggy code on my end. When I updated the script to support a custom frame size, I changed everything but the distance preset function to use that code, so it wasn’t properly determining the frame size it should have been using (in addition to the goof on the trig).

Again, thanks for spotting the bug.

sfc

Hi Jason,

I’ve been scouring the internet and speaking with people, but I’ve not found anyone who knows the answer to my problem. I am working with old (1960) aerial photography and in the software I’m using, I am asked for the 35mm focal Equivalent. I know this typically applies to digital photography, but does it also refer to analog film too? If it does, then how do I calculate it? I am not a photographer, so I’m not certain of all of the terms involved with the camera and film. The camera used was a Fairchild with a Bouche & Lomb lens. The calibrated focal length is ~153mm and the film size is 9×9 inches. The aperture (is that also the ‘f/stop’?) is possibly f/8. The altitude is 20,000 feet. In your calculator above, you list the “Sensor size”? Will that be the same size as the film or something else entirely because this is information that I do not currently have (and trying to find a camera manual hasn’t been the easiest).

I would very much appreciate any time an consideration you have to address this.

Regards,
S

Jason Franke | admin

Hi sfc,

Thanks for the questions, I hope these answers help.

in the software I’m using, I am asked for the 35mm focal Equivalent. I know this typically applies to digital photography, but does it also refer to analog film too?

Yes, the “35mm focal equivalent” applies as a conversion to any size frame that’s not a 24 x 36 mm (“35mm” or full frame digital).

If it does, then how do I calculate it?

You need to determine the ratio between the frame you’re working with and the 35mm frame, then divide the focal length by that ratio. Normally this would be the diagonal of one divided by the diagonal of the other.

However, you may want to use the short edge of the frame (24mm) instead since aspect ratio is different between your square frame and the 3:2-aspect ratio film frame.

My calculator here uses the diagonal of the frame to compute the equivalent focal lengths.

The calibrated focal length is ~153mm and the film size is 9×9 inches.

Since your frame is larger than a 35mm frame, you should expect the 35mm equivelent focal length to be much shorter than the 153 mm specified.

In your calculator above, you list the “Sensor size”? Will that be the same size as the film or something else entirely because this is information that I do not currently have (and trying to find a camera manual hasn’t been the easiest).

Yes, sensor size is the same as film size. More precisely I should probably call it “frame” size as the size as that’s what is really being sought.

Chris

Hi Andrew, I have a question about FOV calculations.

Thank you for this post, it’s been very helpful! I’m writing some code to automate this process, taking sensor size, focal length and object distance as the inputs.

I’ve got to the point where I can calculate the horizontal angle of view from:
2*atan(sensor width/(2*focal length)), that works fine.

I can’t work out how you’re getting from angle of view to the metric field of view (although I know your calculations are correct!)

I’ve been using:

2*object distance*tan(angle/2), but this doesn’t work for some reason.

I might be doing something dumb, but wanted to check first what equation you’re using, if you don’t mind.

Again, thanks for this post!
Best wishes,

Chris

Jason Franke | admin

Hi Chris,

I’m not Andrew, not sure who you’re addressing there, but since this is my site and my code, I’ll be answering your question today. :-)

The equation I use is 2 * object distance * tan(angle of view/2) for the appropriate angle of view (horizontal, vertical, or diagonal).

If you’re not getting the correct results from that, make sure that you’re using the right units for the angle. The trig functions for most, if not all, languages use radians not degrees. Internally my script does all calculations in mm and radians and only converts to degrees and meters or inches to display the value.

Hope that helps.

Artur

Hello Jason,

first of all thank you for that great tool. I tried many DOF-Calculators but yours is nearly perfect. And now my question to make. Is it much of a trouble to include a custom F-Stop function? Most of the lenses I use or try to calculate with have unusual values. I tried to mess with the URL and change the values, but they are obviously not connected to the code.

Best regards,
Artur

Jason Franke | admin

Artur,

It certainly would be possible, but I can’t make any promises as to how quickly I’d be able to get to it. I will add it to my to do list. I am working on adding some new features to the tool currently, so I should be able to fit it in reasonably soon.

Thanks.

terry stahly | terry stahly's Website

I just spent two hours making charts or cheat sheets for my iPhone in Photos a folder I created that is DOF charts for each of my lense on another calcualtor before I found yours and wasted all my time. Before I go through all of that again with yours does the fact that a Sony a7rII is mirrorless affect any of these formulas with EF full frame Sony lenses? Thanks this looks like a real valuable tool I am going to try and load the bookmark for it and see if can to that on my phone or ipad if necessary.

Jason Franke | admin

@Terry Stahly,

Before I go through all of that again with yours does the fact that a Sony a7rII is mirrorless affect any of these formulas with EF full frame Sony lenses?

Being mirrorless or not is not a factor. Since your A7R II is full frame, you can pick “Full Frame/Nikon FX” from the list and go from there.

Jeff Armstrong | Jeff Armstrong's Website

Why would the depth of field of a 6×4.5 with a 105mm f/2.5 framing for the upper body be less than the depth of field of a 6×7 with a 105mm f/2.5 framing for the upper body?

Wouldn’t the 6×7 have shallower depth of field due to the need to be closer to the subject to achieve the same crop as the 6×4.5?

I have tested both, and have found that I must be further from my subject with the 6×4.5 to achieve the same crop as the 6×7. However, the calculator says that I must be equal distance from the subject with both formats to achieve the same upper body crop.

How can this be?

Jason Franke | admin

Hi Jeff,

To answer your last question, “how can this be?” It can be, because I’m an imperfect programmer that reversed width and height values for the 6×7 frame in the the script.

I calculate my “preset subject distances” by using the width of the frame. Since in most cases, the width is the long edge, and since the subjects are “portrait” kinds of images, this usually works fine. The oops is that I seem to have specified 6×7 as 7×6 in the script. So the script was using the same width as 645 and 6×6 when calculating the subject distances. Same width = same distance, and yep, things don’t work right.

Thanks for catching this, I’ve updated the script to put the right dimensions in the right fields.

Paul

Thought you might like to know – I haven’t been able to access your site for a few months. Every time I tried it asked for my Apple ID keychain info! that was on Safari. I’ve just tried on Chrome and it worked. Weird.

Jason Franke | admin

Paul,

I haven’t seen that problem but, I’ll look into seeing if I can figure out what might be causing that.

Tomas Lind

Hi Jason,

Accuracy of field of view for taking pictures at close distances, say less than a few meters.

Thanks for a nice webpage. A great resource. I have a Nikon DX camera with a standard 18-300 mm superzoom lens so I specify “Nikon DX/APS-C (1,53×)” on the webpage.

When calculating field of view the figures for 1 m distance for focal lengths between 18 mm upp to 100 mm the figures given on the webpage are close to what I get when I´m taking pictures of a ruler. Now, When using 300 mm (actual focal length “labeled on the lens”) at 1 m distance the result tells me that 8 cm would fit in horisontally on the Picture. In reality, when taking a picture of a ruler 16 cm fits in! Maybe there are some approximations in the formulas used to calculate the field of view. It would be great if they were closer to reality.

A second question. Does the depth of field, angle of field and field of view results from the webpage also work for macro lenses? (I don´t have any macro but it would be nice to know.)

I very much appreciate your webpage.

Thanks

Tomas

Jason Franke | admin

Hi Tomas,

There area number of factors in real lens designs that can cause the actual behavior of a lens to deviate from the predicted idealized behavior that I’m calculating here. Some of these can become more significant at close focusing distances, and I don’t consider in these calculations (nor do any other DOF calculators that I know of for that matter), largely because the extent of their effect is dependant on the specifics of the design of the lens and I would need to have specific profile information for every possible lens. It’s important to understand that any of these kinds of calculations are idealized and not necessarily going to be reflective of the reality of your specific lens under every specific condition.

For example, internal and rear focusing still photography lenses (your Nikon 18-300 is an internal focusing lens) tend to change focal length, and thus angle of view, when focusing closer than infinity. The listed focal length is only the actual focal length of the lens when the lens is focused at infinity (in my experience they get wider in terms of angle of view).

For example, when I was testing filter holders on ultra-wide angle zooms, a holder might not vignette at 16mm and infinity focus, but would if I focused the lens at the minimum focus distance.

At normal working distances, the changes in focal length from the internal/rear focusing design aren’t that significant. But at the very close end of the focusing range scale, and again depending on the lens, they can be.

Since this error in focal length is specific to each individual lens design, I don’t even attempt to compensate for it in the calculations. Like all DoF calculators, these numbers are more of an ideal than a completely accurate prediction for any specific lens.

As far as macro goes, the calculations should provide a reasonable estimate, but they almost certainly won’t be accurate; again because of the complexities imposed by real lens designs instead of idealized calculations.

Hope that helps explain some of the differences you’re seeing.

May WANG

Hi Jason,

A nice webpage!

I want to know how to get the size of circle of confusion. I googled that the circle of confusion is not a constant value, which is related to focal length,object distance,etc. However in your webpage as the sensor is chosen,the circle of confusion is fixed.

“Distance” in your tools is the distance between object and image plane?

Thanks.

May WANG

Jason Franke | admin

May,

Yes, distance is the distance between the object and image planes.

As for the circle of confusion… To put it simply this is complicated and highly depends on the assumptions you’re going to use and what those assumptions are.

The most commonly used formula for the circle of confusion as it relates to depth of field calculations is `d/1500` where `d` is the diagonal of the frame. This is what the vast majority of camera makers use when they provide depth of field information for their lenses.

That said, there are other formulas, such as “Zeiss formula” which is `d/1730` or the “Kodak formula” which is `f/1720` where `f` is the focal length.

The circle of confusion, is fundamentally a simplification for a much more complex set of assumptions. In very broad strokes, is that the CoC we use is a transformation of the acuity of human vision looking at a print of the image at a specified distance and scaling that down to the size of the film/image sensor. If you’ve cropped your image relative to the full frame size of your format, then the “actual” CoC changes because the magnification ratio from the image to the final print changes. If you change the viewing distance of the final print, then the CoC changes. If you’re viewer has better or worse than average vision, then the CoC changes. Change the viewing distance of the final print, and the CoC changes.

Calculating and dealing with all those variables is not practical to try and figure out every detail, so for depth of field calculations we distill the myriad of variables into something that provides a reasonable approximation across many cases, and use that to calculate the “depth of field”. These are the “standard” circle of confusion values.

Perhaps what may be most important to understand is that depth of field calculations are not precise values with hard physical cut offs and you can’t treat them that way. Depth of field values are at best reasonable estimates of what should be acceptably in focus for a reasonable set of assumptions.

Hope that helps.

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