HELP SECTION

The Depth of Field, Magnification and Close-up Lens Calculator 

The original version comes from Tom Striewisch and was substantially extended by Alexander Kluge. I have now inserted diffraction, the facility for close-up lens values, and the tables. In addition numerous other participants of the group of new de.rec.fotografie have contributed know-how.

References

Enlargement 

As nominal dimensions for picture area were used with 8 x 11 and small pictures, with APS and roll film the appropriate values may be nearer 12,7mm x 30.2mm, 16,7mm x 30,2mm, 16,7mm x 25,5mm, 56mm x 56mm and 56mm x 87mm. Thus picture angles and image fields can possibly deviate somewhat compared with other calculators.    (up)

Circle of confusion 

The diameter of the maximum circle of confusion is determined on the basis of small pictures according to the relationship of the format diagonals.   (up)

Lens 

The calculation of scales, shooting distances and lens extension is based upon symmetrical, rectilinear (non-fish-eye) lenses without internal (or rear) focusing. For all other lenses only reference values can be supplied.

Distance input

The input of the distance values (and a part of the output) refers to the front main element of the lens or, for close-up lenses, the plane of the close-up lens. It does not refer, as indicated on the lens, to the film plane. This is for the following reasons:

(up)

1 - For an object distance starting from the film plane (mostly) two different situations exist. One of the two situations is normally reached only with intermediate rings or bellows. Example: 50mm focal length, object 36cm starting from the film plane, results in a magnification with 1cm extension from 1:5, to one of 25cm extension 5:1. 

2 - The distance to the optical principal planes is unknown for most lenses. To some extent, exact computation with the subject to film-plane distance is therefore impossible.     (up)

Links / Other on-line calculators

Other on-line Calculators:

Original version by Tom Striewisch. Only for small formats: 
www.striewisch-fotodesign.de/lehrgang/anmerk/ts_kb.htm

English calculator with many digital camera formats:
http://www.dofmaster.com/dofjs.html

Documents, Specifications etc.

More on depth of field (by Oliver Jennrich): 104 Kb PDF (Requires Acrobat Reader)

Detailed comments on depth of field and diffraction: http://www.bobwheeler.com/photo/ViewCam.pdf  (Requires Acrobat Reader, English)

How to Select the Sharpest Aperture, Considering Depth of Field and Diffraction http://www.kenrockwell.com/tech/focus.htm (English)

    (up)

Diffraction 

I have assumed that the area of the unsharp circle is additional. (That is only one approximation. Anyone aware of a better solution, and who also knows of a PDF document by Bob Wheeler at http://www.bobwheeler.com/photo/ViewCam.pdf, please call.) 

Details of diffraction also found at: http://homepage.swissonline.ch/severin/foto/foerdble.htm

1. 'Consider diffraction: No' 
   1. For the limiting and optimum apertures, the values that can be set (stopped) are computed rather than the effective aperture. 
   2. The optimum aperture is not further reduced due to the depth of field from diffraction sharpness. 
   3. The diameter of the diffraction circle = effective aperture/1500. 
2. 'Consider diffraction: Yes' 
   1. The diameter of the diffraction circle, and limiting and optimum apertures, are determined as in 1. 
   2. The maximum circle of confusion diameter is calculated from the diameter of the diffraction circle and the given circle of confusion. 
   3. The unmodified depth of field is calculated from the resultant (proportional) circle of confusion. 
   4. The diffraction circle was determined as in 1.b. 
   5. The set unsharp circle exceeds the diameter of the diffraction circle - all the sharpness-related fields (near point, far point etc.) will display 'Diffraction'. 

    (up)

Usages 

Technical terms emphasized in this text are referenced in the glossary and the technical dictionary.   (up)

Details 

In the fields on the left the data needed for the computation of the different values can be input. These are not checked. Every change of an input field or click of the "Update" button produces a new calculation.   (up)

Image format (mandatory) 

If selected, with this photograph format, the usual maximum becomes the circle of confusion and circle of confusion diameters are automatically assigned. In addition, it is determined roughly according to the relationship of the format diagonals, and can be changed at any time. With selection of “Digital” for digital cameras, a jump takes place to "Compute circle of confusion"”, where the conversion factor and the aspect ratio of the digital camera must be entered.   (up)

Focal length (mandatory) 

The focal length of the lens in millimetres. With digital cameras, optionally, an equivalent focal length can be used. A small table also gives a few conversion factors (conversion factor). 

Calculate circle of confusion

Jumps in to the form "Compute circle of confusion" 

Maximum circle of confusion (mandatory) 

Based upon those depths of fields, the maximum permitted diameter for the circles of confusion diffraction on the film (in millimetres). In addition, it is given by the selected format and can, for example for particularly high requirements (large enlargements), be selected manually.     (up)

Diffraction included (Yes/No) 

With the (No) setting, the effects of the two sources of blurring ( diffraction and scatter) are not added to determine the resulting sharpness depth. 

With (Yes), an estimation is made of how large the sharpness depth could be if both sources are considered.   (up)

(To the procedure) 

Minimum focus distance (optional) 

The shortest distance in centimetres (0 for no indication), adjustable at the lens. It is used for the computation of the range of adjustment with a close-up lens.     (up)

Subject Distance (mandatory) 

The distance of sujects from the front principal plane of the lens. For close-up lenses (distance input), this can optionally be entered using metres or centimetres.   (up)

Refractive power of close-up lens (optional) 

The preset (0) stands for non-close-up lens. Every other value indicates the refractive power of an attached close-up lens in dioptres.     (up)

Aperture (mandatory) 

Default preset is aperture f/8. Up to now this was done without smaller increments.     (up)

Depth of Field 

Near point

The distance from the (principal plane of a close-up lens) at which the area of sharpness begins. Everything up to the far point is rendered sharp.     (up)

Far point

The distance from the (principal plane of a close-up lens) at which the sharpness range ends. Everything between this and the near point is rendered sharp.     (up)

Range

Extension of the sharpness range, also the distance between the near point and far point. From the hyperfocal near distance, the sharpness range extends to infinity.   (up)

To adjust the hyperfocal distance

The distance that must be set on the lens to obtain depth of field to infinity.   (up)

..everything from..

Within the limits of the hyperfocal distances the sharpness range begins with this distance and extends to infinity. (up)

Limiting aperture (Set)

If the aperture is decreased to this value, loss of definition due to diffraction exceeds that due to the certified circle of confusion. Aperture may therefore be limited by diffraction before the sharpness range is exceeded.   (up)

Optimum (Set) aperture.

At this value the calculated sharpness range is optimally sharp. If one continues to reduce the aperture, the range becomes larger but the total sharpness decreases due to diffraction. Details Ken Rockwell.(up)

Diffraction Circle

The diameter to which a single one point is expanded by diffraction.     (up)

Magnification and Enlargement 

Picture area and picture angle are only available when a format is provided.     (up)

Picture Angle

The picture angle is calculated from picture width and the given format. Horizontal denotes the longer side, vertical the shorter, and the diagonal is across the picture.   (up)

Picture Area

The size of the picture area at the set distance gives the picture angle.    (up)

Magnification

The magnification is the ratio of the size of the subject to its image on the film.     (up)

Effective aperture

The real aperture given for the extension     (up)

Exposure factor

At this factor for the lens speed (or longer exposure) through the extension.   (up)

Extension

This distance must be subtracted on the lens in order to render the given distance sharply. Normally done by means of distance setting on the lens. If this is not sufficient, the necessary intermediate rings from this value can be measured.   (up)

Approximate distance to film plane

The subject is found at this distance from the film plane. This distance cannot be indicated precisely because it is very dependent upon the lens design. (Distance input ;Principal plane)   (up)

Close-up lens 

When no close-up lens is used, values from a greater distance are duplicated above here.    (up)

Total focal length

The resulting focal length for close-up lens uage.   (up)

Adjustment distance

The lens must be set at approximately this distance to render the subject sharp.(Distance input)   (up)

Near limit

The minimum distance (to close-up lens) at which the close-up lens can be sharp. It is given by the near adjustment limit provided. (Distance input)   (up)

Maximun magnification

The maximum magnification attainable with close-up lens.     (up)

Far Limit

The maximum distance (to close-up lens) at which the close-up lens can be sharp. It comes from the focal length of the close-up lens. (Distance input)   (up)

Minimum magnification

The magnification with close-up lens when set to infinity.     (up)

Circle of confusion and megapixel calculation 

The size of the allowed cirles of confusion has been based on the resolving power of the human eye. If one wants to compute this maximum for any format, one needs the dimensions and the prospective viewing distance of the enlargement. 

Input 

Aspect Ratio

The relationship of the shorter to longer side with digital cameras. It is used for the computation of the image field and the picture angles. After a check within DRF (de.rec.fotografie) and DARD (de.alt.rec.digitalfotografie) the only ratios seem to be 2:3 and 3:4. There should be more, please speak to Erik Krause.    (up)

Conversion factor

The factor with which equivalent focal length can be calculated from the actual focal length of the small-picture digital camera. The same picture is therefore then produced by a small-picture camera. The factor is used to convert the focal length (during input of the KB-equivalent) and the format data, among other things, for the computation of the permissible circles of confusion.
This factor should be taken from the users manual, or be calculated by dividing the KB equivalent focal length by the genuine focal length.
Here is a short list of the models, data from dard and drf:

Model	Factor
Canon D30	1.60
Canon G1	4.86
Canon Powershot Pro 90	5.29
Fuji FinePix 1400 Zoom	6.33
Fuji FinePix 6900	4.49
Kodak DC 4800	4.67
Kodak DC 265	4.77
Minolta Dimage 7	3.94
Nikon Coolpix E950	5.43
Nikon Coolpix E995	4.75
Olympus C 2100 UZ	5.43
Olympus C-2000	5.38
Olympus C3040	4.93
Ricoh RDC-5000	4.78

(up)

Enlargement

The size of the picture and/or the projection in cm. The longer side must be used thus, for example, with an enlargement of 20 x 30 cm 30 is used.     (up)

Viewing distance

The smallest distance from which the picture or projection is to be viewed. The two buttons "optimum" and "usual" supply reference values.     (up)

Normal 
The usual viewing distance that corresponds to the diagonals of the enlargement (calculated by using the longer side and the format of the photograph). This value is the basis of the usual computation of the maximum circles of confusion.  (up)

Optimum 
The optimum viewing distance is that from which the picture appears to the viewer to have the same picture angle as the scene itself. With this viewing distance the relative importance within the picture appears as in reality, and does not change as with wide-angle photographs which are viewed from a large distance. This value depends on the enlargement factor, the photograph format and the focal length of the lens.    (up)

Results 

Enlargement factor

The print fom the negative or the projection of the slide increased in size by this factor.     (up)

Permissable unsharp circle

A healthy human eye sees yet another circular area which appears, when subtending an angular dimension of 2 minutes of arc or less, as a point. Depending upon viewing distance this corresponds to a circle in the observed picture which arises from the size of the maximum permissible blur circle on the film/sensor. 

This field also accepts inputs. When leaving the field the 'necessary megapixels' are updated (eg to recalculate using the value with the given diffraction). Picture detail is still reagrded as sharp if individual pixels are perceived as smaller than or equal to this indistinct circle. It is insignificant whether blurring results from diffraction, or whether the picture detail lies outside of the sharp-focus region (ie - circle of confusion).   (up)

Update

Recalculates according to the formula: "Calculate circle of confusion ".     (up)

Transfer new value

Transfers the calculated blur circle to the field "Maximum circle of confusion" of the form data; and performs a new computation of the depth of field (etc).     (up)

Required Megapixels

A healthy human eye can differentiate two points as such where they are separated by approximately 1 minute of arc. Depending upon viewing distance, this corresponds to a certain resolution in the viewed picture. 

In order to avoid the perception of individual pixels in digital images, at the given viewing distance and given size, the resolution of the picture should exceed a certain level.   (up)

Table Display 

Data

Aperture from, aperture to

The aperture-dependent results (depth of field, hyperfocal distance, diffraction circle, effective aperture) are calculated for these aperture values and also those lying between them.   (up)

Increments

The distance-dependent results are calculated for these steps between distance from and distance to. The incrementation is computed using the reciprocal value of the distance, and should therefore correspond with the steps printed on lens.     (up)

Distance from, distance to

Shortest and longest distances for which the values are calculated. The shortest distance must be larger than the effective focal length.     (up)

Print size

The relative print size for which the HTML-table is provided.     (up)

Units Yes/No

With 'Units - Yes', all measurements and sizes are formatted in m, cm or mm. With 'Units - No', all measurements are imported to a table calculation in mm and given without units.     (up)

Comments

One writes text here (eg lens type etc.) which appears in the second section of the table with the static data.   (up)

Options

Aperture

The two hyperfocal distances each have their own line at the end of the table. If a close-up lens is used, these values are not used.     (up)

Aperture and distance

Sharpness calculation, effective aperture and diffraction circle diameter depend both on the screen value and on the distance and therefore generate an additional line per distance value.   (up)

Distance

All results which depend only on the distance are found in a new column at the end of the table (in the same order).   (up)

Static data

Results and data, which depend neither on picture nor distance, are given in the second section.   (up)

Hints

For all columns and additional lines a short reference is provided below the table. Print size, viewing distance and enlargement factor are indicated only if specified under "calculate circle of confusion" and the calculated circle of confusion is identical with the one specified in the top form..     (up)

Table writing

The program opens a new browser window to write the table.     (up)

Glossary 

Magnification The ratio of the size of the subject to the size of its illustrated image on the film. When the picture is later enlarged, the total magnification is obtained by multiplying by the enlargement factor.   (back)

Diffraction Light which passes close to an edge is diverted from it. The smaller the aperture opening, the larger the portion of the light deflected at the diaphragm blade. A single point thus becomes a small wafer with indistinct edges. (Calculate)   (back)

Principal planes The planes in the lens starting from which the focal length is measured. Lenses usually have two principal planes, the positions of which are dependent upon the lens design. For accurate computations however it should be admitted that some values are therefore uncertain.     (back)

Internal focusing is defined (here) as a technology which achieves focus by moving only one or more internal groups of lens elements rather than the whole lens. Such lenses often change their focal length when focusing.   (back)

Close-up lens Supplementary lens which acts almost as a magnifying glass when placed in front of the actual lens.   (back)

Rectilinear - A characteristic of a lens to render straight lines and angles as such. A fish-eye lens is an example of a non-rectilinear lens.     (back)

Depth of field The range of distances over which an image appears sharp.   (back)

Symmetrical Lens A lens having a symmetrical arrangement and sequence of elements. With small-picture lenses only a focal length of approximately 50mm is realizable.   (back)

Circle of confusion A point of light which passes through the lens effectively approaches the film in a cone, at the apex of which the film should lie if the point of light is to be resolved as a point. If the film lies film uniformly before or behind this apex, a point is recorded as a circular area. The maximum circle of confusion is the diameter in metres of these circles which are still regarded subjectively as points.   (back)

Version history 

Tom Striewisch:    (up)

• Original version (see also another calculator)

Alexander Kluge:    (up)

• Three columned, comments, hyperfocal distance, magnification modified,
• Recalculate on onBlur instead of onChange
• Picture angle horizontal and vertical corrected.
• Close-up lens to 0.3, then from 0.3.1 automatically formatted in centimetres or metres for picture area. (ie format depends on value.)
• 0.3.5 First published version
• 0.3.6 Distance to film plane
• 0.3.7 APS error message removed
• New version see other calculators

Erik Krause:    (up)

• 0.3.8ß Diffraction blur included.
• 0.3.9ß Correction for diffraction diameter increment.
• 0.3.10ß Hyperfocal calculation now with resultant circle of confusion, optimal aperture inserted.
• 0.3.11ß Correction factor for close-up lens included.
• 0.3.12 Adaptation for Javascript 1.0, for calculation unrounded focal length will be used.
• 0.4.0ß Close-up lens correction, focus adjustment and magnification limit, help for use, glossary...
• 0.4.1ß Failure link and (up) integrated
• 0.4.2ß IE-compatible, will check input numerals
• 0.5.0ß Circle of confusion calculation
• 0.6.0ß Table output
• 0.6.1ß Typeface for table output
• 0.6.2ß Help for table output, obj.clear (a javascript function)
• 0.6.3ß Code tightened (arrays), Bugfix in angle calculation.
• 0.7.0ß Digital factor, table output without units, distance from and to stop given.
• 0.7.1ß Handling for input errors improved (capitals removed, comma replaced).
• 0.7.2ß Bugfix: All output fields read-only, internal links corrected.
• 0.7.3ß Output sharpness range, layout reorganized.
• 0.7.4 Bugfix: Calculation of hyperfocal distance corrected, "Distance" is now "Article width", Input check improved.
• 0.8.0 Optimum aperture now gives the best aperture for sharpness, as described by Ken Rockwell. Aperture instead of radio buttons with drop-down list realization and upgraded to f/64. Download link.
• 0.8.1 Bugfix: Inadvertent index used instead of aperture value, aperture to f/128 included.
• 0.8.2 Bugfix: Correction for optimum aperture for close-up lens, 13 x 18cm to be added, help completed.
• 0.8.3 Bugfix: Picture angle for variable distance (special to close-up lens) corrected.
• 0.8.4 Bugfix: Request for aperture and error message for circle of confusion corrected.
• 0.8.5 'Requires Megapixels' incorporated, background brighter.
• 0.8.6 Read-only fields now in IE grey, links to other calculators included.
• 0.8.7 Colour and layout written in another light sans serif font (CSS).
• 0.8.8 Bugfix: Given input for circle of confusion was not used to compute circle of confusion.
• 0.8.9 Slight layout correction.
• 0.8.10 Outputs fields for IE finally grey!
• 0.8.11 Optimum and limiting apertures (Set) as well as correction for macro diffraction circle, link update, no output if unsharp for close-up lens.
• 0.8.12 Half aperture stops, more CSS
• 0.8.13 Errors when using close-up lens corrected.
• 0.8.13E English language version of 0.8.13 above.
• 0.8.13Ea Correct format problems in help section related to automated translation in to other languages.
• 0.8.13Eb Minor updates for formatting and links.

(up)

 March 2008 

Erik Krause

German version translated to English by The Open Photographic Society - May 2009

0.8.13Eb - Minor updates - 10 May 2016