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Tell your friends about us!Depth of Field Tables
- Thread starter lensman
- Start date
odklizec
PK
Hi David,
Try this online DoF calculator...
http://www.dofmaster.com/dofjs.html
There are all Ricoh cameras (except GXR A12 and S10). The GRDII focal length equivalent of 21mm is 4.4mm. The closest value in DoF calculator is 4.5mm. Hope this helps?
Try this online DoF calculator...
http://www.dofmaster.com/dofjs.html
There are all Ricoh cameras (except GXR A12 and S10). The GRDII focal length equivalent of 21mm is 4.4mm. The closest value in DoF calculator is 4.5mm. Hope this helps?
odklizec
PK
David, I believe it will be the same. The diffraction limit is mainly dependent of sensor size and aperture. The angle of view has only small (if any) impact. But the best would be to try GRDII+GW1 at all apertures. Just try to take the same scene with different apertures (best from tripod and with selftimer to prevent shaking caused by pressing the shutter). I'm sure you will notice no or very minor softness up to f5.6.
BTW, if you are interested to read more about diffraction problem, see this excellent article:
http://www.cambridgeincolour.com/tutori ... graphy.htm
BTW, if you are interested to read more about diffraction problem, see this excellent article:
http://www.cambridgeincolour.com/tutori ... graphy.htm
Detail Man
New Member
Calculating Actual DOF for DigiCams with Computer Displays
.
The "DOF Master" DOF Calculator is the best available that I (personally) have found so far on the internet (that, as Odklizec previously noted) is at:
http://www.dofmaster.com/dofjs.html
The mathematical identities utilized in it's operation are consistent with the identities and derivations found in the excellent (albeit formidable) paper at:
http://www.largeformatphotography.info/ ... nDepth.pdf
Although the multi-lens-systems of digital cameras are likely not precisely equivalent to a single "symmetrical lens", they attempt to approximate (and DOF Calculators assume) that condition.
In using those same identities in order to write/develop a program (for use on my HP-71B Palmtop) that calculates the "object-space" Depth of Field for my various cameras, some important and significant complicating issues presented themselves that I am sharing here - in order that users of the "DOF Master" DOF may be able to use it (or, to alternatively accurately calculate the actual DOF themselves) in order to obtain a numerical result that most closely represents the modern situation of a solid-state image sensor in a digital (not 35mm film) camera, and viewed on a computer's CRT monitor or LCD falt-screen display using a particular "screen-size" in pixels.
The derivation of the diameter of the "Circle of Confusion" (COC) that the DOF Calculator is based upon derives from the 35mm film format days - when the COC diameter was (essentially) determined by exposed vertical height (the smaller dimension in 4:3 aspect ratio) of the 35mm film surface divided by a number representing (essentially) the maximum number of vertical "dots" that some given printing process referenced could be counted upon to individually represent.
As a result of these (still followed) conventions, if (for instance) your camera is not listed in the DOF Calculator database, then one needs to determine the COC for their particular (non-listed) camera. This leads to the additional web-page at the "DOF Master" site:
http://www.dofmaster.com/digital_coc.html
where one finds a listing of the "COC" for a (larger) number of camera models,
where the value derived is based upon the following assumptions:
"The circles of confusion above were calculated using the formula:
CoC = (CoC for 35mm format) / (Digital camera lens focal length multiplier)"
and
"The focal length multiplier for a camera is specified by the manufacturer, or is calculated using the formula:
Multiplier = (35mm equivalent lens focal length) / (Actual lens focal length)"
The list states that my DMC-LX3 has a COC of 0.006 milliMeters (mm).
An examination of the "COC Calculator" (below the list, nears the bottom of the web-page) used to calculate the COC values on the list states (in its footnotes):
"The normal range for 35mm format circle of confusion is 0.025 - 0.035 mm. The Leica standard circle of confusion for 35mm format is 0.025 mm."
These basic numerical figures (unfortunately) are conventions that derive from 35mm film format "image sensors" (so to speak) and photo-printing quality standards. I do not intend here to make definitive statements about the current "state of the art" of professional (or your own printer's) photo-printing. I am here addressing the (often more common, perhaps) actual situation of the image being displayed and viewed on a computer display (either CRT, or LCD flat-screen) after being imaged by the (actual) active vertical height of a (rather tiny, in most cases) solid-state image sensor.
The relevant numbers required to calculate the (more relevant, and more representative) COC (in milliMeters) as it applies to the above described situation requires that one determine two numbers:
(1) The number of pixels represented in the vertical dimension of one's computer display when you view the image (as it is configured by your computer operating system, and supported by your video card and your computer CRT monitor, or LCD flat-screen display). For a full-screen view, this will typically be something like 600 pixels, 768 pixels, 1080 pixels, 1200 pixels, etc.; and
(2) The (actual) active vertical height of the image sensor utilized in your digital camera for the "quality" (pixel-size) that one is shooting at - which is typically significantly less than the amount that one would calculate from the manufacturer's advertised (outer-size) of the image sensor. However, one needs only to determine (and multiply) two specific numbers:
(a) The vertical number of pixels of the digital image that you are recording on the camera; and
(b) The "pixel-pitch" (the distance between the individual pixels) of the particular image-sensor the camera uses.
In example, the DMC-LX3 (in 10 Mpixel mode; 4:3 aspect ratio) uses 2736 pixels
( see: http://www.seriouscompacts.com/2008/07/ ... s-and.html ), and
the DMC-LX3 image sensor (according to Panasonic) has a 2.025 micron (0.002025 mm) pixel-pitch
( see: http://www.panasonic.net/avc/lumix/popu ... ering.html ).
Therefore, the active vertical dimension of the DMC-LX3 image sensor (in 10 Mpixel mode; 4:3 aspect ratio) equals 5.5404 mm.
Using the presently common maximum 1080 pixel-height of LCD flat-screens, the calculation of COC in this case is as follows:
COC = (Active Vertical Dimension of Image Sensor) / (Pixel-Height used to Display the Image)
substituting the numbers (derived above):
COC = (5.5404 mm) / (1080 pixels) = 0.00513 mm
One might say, "well, 0.00513 mm is pretty close to the 0.006 mm shown on the on the list for the DMC-LX3, anyway" ... However, consider the case of my own computer display (1200 pixel-height), which yields a COC of 0.00462 mm. At the macro end, (focusing at less than about 2 Feet) the difference in the result of the DOF calculation (between the COC being either 0.00513 mm or 0.00462 mm) will be in error by a factor inversely proportional to the ratio of these two numbers. Not so bad. However, the sensitivity of the errors resulting from inaccurate values of the COC increases very significantly as the focus-distance increases When focusing at 5.0 Feet (at distances approaching the hyper-focal distance), this (seemingly minor) difference (between the COC being either 0.00513 mm or 0.00462 mm) makes the difference between obtaining a result of DOF equaling 32.0 Feet (for a 1200 pixel display-height) or 102 feet (for 1080 pixel display-height)! Thus, determining the most accurate (actual) value of the COC in your situation can make a very significant difference in the validity of the results of a DOF calculation!
The above calculated high sensitivity of the Depth of Field calculated at sensor-subject distances existing near the Hyper-Focal Distance (of 32 Feet when viewed with a 1200 Pixel display-height, and 102 Feet when viewed with a 1080 Pixel display-height) is the result of the DMC-LX3 operating at a F-Number of 3.2.
The percentage difference is lessened for the case of F=2.8 (18.2 Feet, and 30.0 Feet, respectively).
The percentage difference is further lessened for the case of F=2.0 (7.60 Feet, and 9.35 Feet, respectively).
In the calculation of the "Hyper-Focal Distance", the errors in specifying the "Circle of Confusion" are direct on a percentage basis (not amplified).
Thus, in the case that the distance (from image sensor to focus-plane) is approaching the "Hyper-Focal Distance", and/or the F Number is increased (as is often the case when one is attempting to obtain high "Depth of Field" in a shot), even small percentage errors in the specification of the value of the "Circle of Confusion" can and do result in much larger percentage errors in the "Depth of Field" calculated as a result! (in my viewpoint), there are enough (other) factors (such as optical imperfections of the lens-system, and over-aggressive noise-reduction algorithms smearing details in the far-field of the image) already that may imbue a "false sense of available Depth of Field" in the photographer's mind. Thus, it is helpful to ensure accuracy in calculating the (theoretical) DOF available. These are not moot issues to a photographer (such as myself) who wishes to resolve "far-field" foliage in landscape shots (as opposed to ending up with amorphous blobs of mush) ... :cry:
It would be very helpful if the "DOF Master" DOF Calculator (either) implemented more choices in their "drop-down" menu, or (alternatively, and ideally) allowed for direct entry of the value of the "Circle of Confusion", where the value could be specified to several digits precision beyond the decimal-point ...
Now that my treatise above may have convinced you that the difference (in the COC size) between (for instance) 0.004 mm, 0.005 mm, and 0.006 mm can make a very significant difference in the accuracy of the DOF calculation (a directly-related error at "macro" distances, and an increasing significant degree of error as the focusing-distance increases towards the hyper-focal distance), I regretfully report that the resolution of the choices possible in the "DOF Master" DOF Calculator (once your actual relevant COC is directly determined, in the interest of achieving much better accuracy in the DOF calculation) is no more precise than "0.004 mm, 0.005 mm, 0.006mm", etc. ...... And, if there is an online DOF calculator that allows for the COC value to be entered with several digits of precision, I am not aware of it (though perhaps one does exist, and I am simply not aware of it). If you find one, please post its internet URL on this discussion thread!
The best that I can do for this situation is to state the precise algebraic identities (for full wide-angle at Zoom Factor = 1.0, derived from Conrad's "Depth of Field in Depth" paper, "Object-Side Relationships" section, starting on Page 15 of 45 of the PDF document) that I use in my own developed and well-tested program (appearing below). Note: In order for these (or any) DOF-related algebraic identities to be valid for a digital image sensor, the calculated COC must be larger in size than the size of two pixels (because a "Bayer-array" contains twice as many individual Green photo-sensors as individual Red or Blue photo-sensors). Thus (for the 2.025 micron pixel-pitch of the DMC-LX3 image sensor), the calculated COC must be either equal to, or greater than, 4.05 microns (equal to 0.00405 mm). This would correspond to maximum value of (vertical) display pixel-height of 1368 pixels (presently not available in common present-day monitors/displays).
The algebraic identities:
Distance (between the sensor and the focused-on-subject) of the "Near Limit" of focus = ( (D)*(L^2) ) / ( ( L^2) + (F)*(H)*(D-L) / P )
Distance (between the sensor and the focused-on-subject) of the "Far Limit" of focus = ( (D)*(L^2) ) / ( ( L^2) - (F)*(H)*(D-L) / P )
The "Hyper-Focal Distance" (between the sensor and the focused-on-subject) = (P) / ( F) / (H) ) * (L^2) ) + L
Where the independent variables below are in units of METERS, and:
D is the distance between the image sensor and the focused-on-subject.
L is the actual (not the 35 mm equivalent) Focal Length of the lens-system (at full wide-angle).
F if the F-Number (a dimensionless number).
H is the active (vertical) height of the image sensor being used.
P is the (vertical) number of pixels used to display the image.
The Depth of Field (DOF) is simply the algebraic difference (subtraction) of the two results (the combined algebraic identity is very long and hard to read).
If the value of the "Far Limit" of focus equals a value that is (either) less than or equal to zero, then the "Far Limit" of Focus (and the DOF) is (theoretically) "infinite".
While it may seem from the above that "the devils are in the details" ... :twisted: ... fear not - so is (also a greater degree of) accurate truths ...
.
.
The "DOF Master" DOF Calculator is the best available that I (personally) have found so far on the internet (that, as Odklizec previously noted) is at:
http://www.dofmaster.com/dofjs.html
The mathematical identities utilized in it's operation are consistent with the identities and derivations found in the excellent (albeit formidable) paper at:
http://www.largeformatphotography.info/ ... nDepth.pdf
Although the multi-lens-systems of digital cameras are likely not precisely equivalent to a single "symmetrical lens", they attempt to approximate (and DOF Calculators assume) that condition.
In using those same identities in order to write/develop a program (for use on my HP-71B Palmtop) that calculates the "object-space" Depth of Field for my various cameras, some important and significant complicating issues presented themselves that I am sharing here - in order that users of the "DOF Master" DOF may be able to use it (or, to alternatively accurately calculate the actual DOF themselves) in order to obtain a numerical result that most closely represents the modern situation of a solid-state image sensor in a digital (not 35mm film) camera, and viewed on a computer's CRT monitor or LCD falt-screen display using a particular "screen-size" in pixels.
The derivation of the diameter of the "Circle of Confusion" (COC) that the DOF Calculator is based upon derives from the 35mm film format days - when the COC diameter was (essentially) determined by exposed vertical height (the smaller dimension in 4:3 aspect ratio) of the 35mm film surface divided by a number representing (essentially) the maximum number of vertical "dots" that some given printing process referenced could be counted upon to individually represent.
As a result of these (still followed) conventions, if (for instance) your camera is not listed in the DOF Calculator database, then one needs to determine the COC for their particular (non-listed) camera. This leads to the additional web-page at the "DOF Master" site:
http://www.dofmaster.com/digital_coc.html
where one finds a listing of the "COC" for a (larger) number of camera models,
where the value derived is based upon the following assumptions:
"The circles of confusion above were calculated using the formula:
CoC = (CoC for 35mm format) / (Digital camera lens focal length multiplier)"
and
"The focal length multiplier for a camera is specified by the manufacturer, or is calculated using the formula:
Multiplier = (35mm equivalent lens focal length) / (Actual lens focal length)"
The list states that my DMC-LX3 has a COC of 0.006 milliMeters (mm).
An examination of the "COC Calculator" (below the list, nears the bottom of the web-page) used to calculate the COC values on the list states (in its footnotes):
"The normal range for 35mm format circle of confusion is 0.025 - 0.035 mm. The Leica standard circle of confusion for 35mm format is 0.025 mm."
These basic numerical figures (unfortunately) are conventions that derive from 35mm film format "image sensors" (so to speak) and photo-printing quality standards. I do not intend here to make definitive statements about the current "state of the art" of professional (or your own printer's) photo-printing. I am here addressing the (often more common, perhaps) actual situation of the image being displayed and viewed on a computer display (either CRT, or LCD flat-screen) after being imaged by the (actual) active vertical height of a (rather tiny, in most cases) solid-state image sensor.
The relevant numbers required to calculate the (more relevant, and more representative) COC (in milliMeters) as it applies to the above described situation requires that one determine two numbers:
(1) The number of pixels represented in the vertical dimension of one's computer display when you view the image (as it is configured by your computer operating system, and supported by your video card and your computer CRT monitor, or LCD flat-screen display). For a full-screen view, this will typically be something like 600 pixels, 768 pixels, 1080 pixels, 1200 pixels, etc.; and
(2) The (actual) active vertical height of the image sensor utilized in your digital camera for the "quality" (pixel-size) that one is shooting at - which is typically significantly less than the amount that one would calculate from the manufacturer's advertised (outer-size) of the image sensor. However, one needs only to determine (and multiply) two specific numbers:
(a) The vertical number of pixels of the digital image that you are recording on the camera; and
(b) The "pixel-pitch" (the distance between the individual pixels) of the particular image-sensor the camera uses.
In example, the DMC-LX3 (in 10 Mpixel mode; 4:3 aspect ratio) uses 2736 pixels
( see: http://www.seriouscompacts.com/2008/07/ ... s-and.html ), and
the DMC-LX3 image sensor (according to Panasonic) has a 2.025 micron (0.002025 mm) pixel-pitch
( see: http://www.panasonic.net/avc/lumix/popu ... ering.html ).
Therefore, the active vertical dimension of the DMC-LX3 image sensor (in 10 Mpixel mode; 4:3 aspect ratio) equals 5.5404 mm.
Using the presently common maximum 1080 pixel-height of LCD flat-screens, the calculation of COC in this case is as follows:
COC = (Active Vertical Dimension of Image Sensor) / (Pixel-Height used to Display the Image)
substituting the numbers (derived above):
COC = (5.5404 mm) / (1080 pixels) = 0.00513 mm
One might say, "well, 0.00513 mm is pretty close to the 0.006 mm shown on the on the list for the DMC-LX3, anyway" ... However, consider the case of my own computer display (1200 pixel-height), which yields a COC of 0.00462 mm. At the macro end, (focusing at less than about 2 Feet) the difference in the result of the DOF calculation (between the COC being either 0.00513 mm or 0.00462 mm) will be in error by a factor inversely proportional to the ratio of these two numbers. Not so bad. However, the sensitivity of the errors resulting from inaccurate values of the COC increases very significantly as the focus-distance increases When focusing at 5.0 Feet (at distances approaching the hyper-focal distance), this (seemingly minor) difference (between the COC being either 0.00513 mm or 0.00462 mm) makes the difference between obtaining a result of DOF equaling 32.0 Feet (for a 1200 pixel display-height) or 102 feet (for 1080 pixel display-height)! Thus, determining the most accurate (actual) value of the COC in your situation can make a very significant difference in the validity of the results of a DOF calculation!
The above calculated high sensitivity of the Depth of Field calculated at sensor-subject distances existing near the Hyper-Focal Distance (of 32 Feet when viewed with a 1200 Pixel display-height, and 102 Feet when viewed with a 1080 Pixel display-height) is the result of the DMC-LX3 operating at a F-Number of 3.2.
The percentage difference is lessened for the case of F=2.8 (18.2 Feet, and 30.0 Feet, respectively).
The percentage difference is further lessened for the case of F=2.0 (7.60 Feet, and 9.35 Feet, respectively).
In the calculation of the "Hyper-Focal Distance", the errors in specifying the "Circle of Confusion" are direct on a percentage basis (not amplified).
Thus, in the case that the distance (from image sensor to focus-plane) is approaching the "Hyper-Focal Distance", and/or the F Number is increased (as is often the case when one is attempting to obtain high "Depth of Field" in a shot), even small percentage errors in the specification of the value of the "Circle of Confusion" can and do result in much larger percentage errors in the "Depth of Field" calculated as a result! (in my viewpoint), there are enough (other) factors (such as optical imperfections of the lens-system, and over-aggressive noise-reduction algorithms smearing details in the far-field of the image) already that may imbue a "false sense of available Depth of Field" in the photographer's mind. Thus, it is helpful to ensure accuracy in calculating the (theoretical) DOF available. These are not moot issues to a photographer (such as myself) who wishes to resolve "far-field" foliage in landscape shots (as opposed to ending up with amorphous blobs of mush) ... :cry:
It would be very helpful if the "DOF Master" DOF Calculator (either) implemented more choices in their "drop-down" menu, or (alternatively, and ideally) allowed for direct entry of the value of the "Circle of Confusion", where the value could be specified to several digits precision beyond the decimal-point ...
Now that my treatise above may have convinced you that the difference (in the COC size) between (for instance) 0.004 mm, 0.005 mm, and 0.006 mm can make a very significant difference in the accuracy of the DOF calculation (a directly-related error at "macro" distances, and an increasing significant degree of error as the focusing-distance increases towards the hyper-focal distance), I regretfully report that the resolution of the choices possible in the "DOF Master" DOF Calculator (once your actual relevant COC is directly determined, in the interest of achieving much better accuracy in the DOF calculation) is no more precise than "0.004 mm, 0.005 mm, 0.006mm", etc. ......
And, if there is an online DOF calculator that allows for the COC value to be entered with several digits of precision, I am not aware of it (though perhaps one does exist, and I am simply not aware of it). If you find one, please post its internet URL on this discussion thread!The best that I can do for this situation is to state the precise algebraic identities (for full wide-angle at Zoom Factor = 1.0, derived from Conrad's "Depth of Field in Depth" paper, "Object-Side Relationships" section, starting on Page 15 of 45 of the PDF document) that I use in my own developed and well-tested program (appearing below). Note: In order for these (or any) DOF-related algebraic identities to be valid for a digital image sensor, the calculated COC must be larger in size than the size of two pixels (because a "Bayer-array" contains twice as many individual Green photo-sensors as individual Red or Blue photo-sensors). Thus (for the 2.025 micron pixel-pitch of the DMC-LX3 image sensor), the calculated COC must be either equal to, or greater than, 4.05 microns (equal to 0.00405 mm). This would correspond to maximum value of (vertical) display pixel-height of 1368 pixels (presently not available in common present-day monitors/displays).
The algebraic identities:
Distance (between the sensor and the focused-on-subject) of the "Near Limit" of focus = ( (D)*(L^2) ) / ( ( L^2) + (F)*(H)*(D-L) / P )
Distance (between the sensor and the focused-on-subject) of the "Far Limit" of focus = ( (D)*(L^2) ) / ( ( L^2) - (F)*(H)*(D-L) / P )
The "Hyper-Focal Distance" (between the sensor and the focused-on-subject) = (P) / ( F) / (H) ) * (L^2) ) + L
Where the independent variables below are in units of METERS, and:
D is the distance between the image sensor and the focused-on-subject.
L is the actual (not the 35 mm equivalent) Focal Length of the lens-system (at full wide-angle).
F if the F-Number (a dimensionless number).
H is the active (vertical) height of the image sensor being used.
P is the (vertical) number of pixels used to display the image.
The Depth of Field (DOF) is simply the algebraic difference (subtraction) of the two results (the combined algebraic identity is very long and hard to read).
If the value of the "Far Limit" of focus equals a value that is (either) less than or equal to zero, then the "Far Limit" of Focus (and the DOF) is (theoretically) "infinite".
While it may seem from the above that "the devils are in the details" ... :twisted: ... fear not - so is (also a greater degree of) accurate truths ...
.
Detail Man
New Member
Interesting Info: Sweet-Spots and Diffraction-Limited-Apertu
.
The aperture (F-Number) setting at which a lens-system's "sweet-spot" exists may well involve various optical aberrations and other non-ideal effects, (potentially) placing the perceived "sweet-spot" at a higher F-Number than the calculation of "diffraction-limited-aperture" would imply.
At least, according to the interesting April 13, 2008, 3:44 AM post by "McQ" on this rather interesting discussion thread at:
http://www.cambridgeincolour.com/forums/thread15.htm
where "McQ" states:
"One particularly important concept is the difference between the diffraction limit and a lens's 'sweet spot', which can be very crudely described as the optimum aperture which minimizes the sum total contribution of both diffraction and aberrations. Unless your lens is a perfectly designed lens (aka diffraction limited lens), often times aberrations play more of a role than diffraction when determining your sweet spot. This effectively means that the sweet spot is located at a narrower aperture than the diffraction limit." ...
and
" ... often times the appearance of a sharp, clear image is more dictated by small-scale local contrast (MTF50) than by absolute resolution. Local contrast can in fact improve slightly beyond the diffraction limit, even if absolute resolution decreases. Further, in-camera sharpening tricks, Bayer conversion and other post-processing in-camera can mean that having an airy disc slightly larger than the pixel size will not be as noticeable, and therefore one can push the aperture narrower than one would ordinarily calculate."
Regarding the calculation of the F-Number at (and above which) "diffraction-limited-aperture" exists in a lens-system:
The "Diffraction Limit Calculator" on the web-page at:
http://www.cambridgeincolour.com/tutori ... graphy.htm
appears to likely utilize the following algebraic identity (to calculate the diameter of the first dark diffraction ring of the "Airy disk"):
D = ( 2.44 ) * ( "lamba"; wavelength in Meters) * (F-Number)
which (at the 550 nanoMeter wavelength center of the visible spectrum) yields:
D = (1.342 microMeters) * (F-Number)
A good web-page discussing these relationships is at:
http://www.astro-imaging.de/astro/wavelength.html
In example, if the "Circle of Confusion" (COC) on the DMC-LX3 is assumed to be (exactly) two pixels in size (0.00405 mm), then the threshold for "diffraction-limited-aperture" would appear to begin at (or above) an F-Number of 3.0179 (between the possible F-Number settings of 2.8 and 3.2). However, if a DMC-LX3 image is dispalyed (full-screen) on a computer LCD flat-screen display with a vertical pixel-height having the common value of 1080 pixels (with the COC calculated as 0.00513 mm in the above post entitled, "Calculating Actual DOF for DigiCams with Computer Displays"), the diameter of the "Airy disk" would not exceed the the COC until a DMC-LX3 F-Number of 3.8227 or greater is reached (above the available F-Number setting of 3.5, and at F=4.0).
Interestingly, in the following DMC-LX3 review at:
http://www.luminous-landscape.com/revie ... /lx3.shtml
the reviewer states:
"By f/4 the lens is at its "sweet spot" and leaves little to be desired in terms of overall image quality."
Considering the statement (in the first post referenced above) about lens-system optical aberrations and other non-ideal effects increasing the F-Number at which the opined "sweet-spot" exists, these findings (of the "sweet-spot" existing barely above the theoretical "diffraction-limited-aperture" F-Number for a 1080 pixel-height display size) appear to say very good things about the overall quality of the DMC-LX3's Leica lens-system!
In that the subject (of the first post referenced above) concerns the much larger-sized and lager diameter Leica lens systems employed in the DMC-FZ30 and DMC-FZ50 (and the apparent elevation of the F-Number at which the "sweet-spot" exists for those camera models), perhaps the fact that the maximum Zoom Factor was set at a maximum value of x2.5 in the case DMC-LX3 (as opposed to a maximum value of x12.0 in the FZ30/50) assists Panasonic in the taming of such aberrations and other non-ideal effects. This all seems quite impressive for such a compact package, indeed ...
.
.
The aperture (F-Number) setting at which a lens-system's "sweet-spot" exists may well involve various optical aberrations and other non-ideal effects, (potentially) placing the perceived "sweet-spot" at a higher F-Number than the calculation of "diffraction-limited-aperture" would imply.
At least, according to the interesting April 13, 2008, 3:44 AM post by "McQ" on this rather interesting discussion thread at:
http://www.cambridgeincolour.com/forums/thread15.htm
where "McQ" states:
"One particularly important concept is the difference between the diffraction limit and a lens's 'sweet spot', which can be very crudely described as the optimum aperture which minimizes the sum total contribution of both diffraction and aberrations. Unless your lens is a perfectly designed lens (aka diffraction limited lens), often times aberrations play more of a role than diffraction when determining your sweet spot. This effectively means that the sweet spot is located at a narrower aperture than the diffraction limit." ...
and
" ... often times the appearance of a sharp, clear image is more dictated by small-scale local contrast (MTF50) than by absolute resolution. Local contrast can in fact improve slightly beyond the diffraction limit, even if absolute resolution decreases. Further, in-camera sharpening tricks, Bayer conversion and other post-processing in-camera can mean that having an airy disc slightly larger than the pixel size will not be as noticeable, and therefore one can push the aperture narrower than one would ordinarily calculate."
Regarding the calculation of the F-Number at (and above which) "diffraction-limited-aperture" exists in a lens-system:
The "Diffraction Limit Calculator" on the web-page at:
http://www.cambridgeincolour.com/tutori ... graphy.htm
appears to likely utilize the following algebraic identity (to calculate the diameter of the first dark diffraction ring of the "Airy disk"):
D = ( 2.44 ) * ( "lamba"; wavelength in Meters) * (F-Number)
which (at the 550 nanoMeter wavelength center of the visible spectrum) yields:
D = (1.342 microMeters) * (F-Number)
A good web-page discussing these relationships is at:
http://www.astro-imaging.de/astro/wavelength.html
In example, if the "Circle of Confusion" (COC) on the DMC-LX3 is assumed to be (exactly) two pixels in size (0.00405 mm), then the threshold for "diffraction-limited-aperture" would appear to begin at (or above) an F-Number of 3.0179 (between the possible F-Number settings of 2.8 and 3.2). However, if a DMC-LX3 image is dispalyed (full-screen) on a computer LCD flat-screen display with a vertical pixel-height having the common value of 1080 pixels (with the COC calculated as 0.00513 mm in the above post entitled, "Calculating Actual DOF for DigiCams with Computer Displays"), the diameter of the "Airy disk" would not exceed the the COC until a DMC-LX3 F-Number of 3.8227 or greater is reached (above the available F-Number setting of 3.5, and at F=4.0).
Interestingly, in the following DMC-LX3 review at:
http://www.luminous-landscape.com/revie ... /lx3.shtml
the reviewer states:
"By f/4 the lens is at its "sweet spot" and leaves little to be desired in terms of overall image quality."
Considering the statement (in the first post referenced above) about lens-system optical aberrations and other non-ideal effects increasing the F-Number at which the opined "sweet-spot" exists, these findings (of the "sweet-spot" existing barely above the theoretical "diffraction-limited-aperture" F-Number for a 1080 pixel-height display size) appear to say very good things about the overall quality of the DMC-LX3's Leica lens-system!
In that the subject (of the first post referenced above) concerns the much larger-sized and lager diameter Leica lens systems employed in the DMC-FZ30 and DMC-FZ50 (and the apparent elevation of the F-Number at which the "sweet-spot" exists for those camera models), perhaps the fact that the maximum Zoom Factor was set at a maximum value of x2.5 in the case DMC-LX3 (as opposed to a maximum value of x12.0 in the FZ30/50) assists Panasonic in the taming of such aberrations and other non-ideal effects. This all seems quite impressive for such a compact package, indeed ...
.
Detail Man
New Member
Numerical Corrections: Actual DOF for DigiCams
Text of the original post above on this thread ("Calculating Actual DOF for DigiCams with Computer Displays") was edited to reflect corrections/clarifications.
Text of the original post above on this thread ("Calculating Actual DOF for DigiCams with Computer Displays") was edited to reflect corrections/clarifications.
Detail Man
New Member
Further Clarification - Actual DOF for Digicams
Text of the original post above on this thread ("Calculating Actual DOF for DigiCams with Computer Displays") was edited to reflect corrections/clarifications.
Text of the original post above on this thread ("Calculating Actual DOF for DigiCams with Computer Displays") was edited to reflect corrections/clarifications.
Detail Man
New Member
Here you go, Lensman.
These are results for your 768 pixel-height display screen-size. A caveat. While this may seem counter-intuitive - the Depth of Field (DOF) actually decreases with increasing monitor/display screen-sizes (in pixels). Keep that in mind if you are considering full-sized (or slightly cropped) images out of camera, or as they are previewed in a ("raw", TIF, or JPG) post-processor, or if you are producing final JPGs for display that are larger than 1024x768 ...
This is the "object-space" DOF for a symmetrical lens. The multiple lens-systems in our cameras (as I understand it) approximate that condition. As an "object-space" calculation, it assumes the "worst-case scenario" - that the viewer is viewing the monitor/display (whatever it's physical size may be), "up-close".
It is not important whether the viewed 768 pixel-height image fills the entire monitor/display screen, or just fills a portion of the monitor/display screen's size (in pixels). It is not important how physically large the monitor/display screen is. Since it is assumed that the viewer is "up-close", all that matters is that the viewed image is 768 pixels in height. It does not matter whether the horizontal pixel-size of the image is 1024 pixels (or more than 1024 pixels). The Depth of Field is derived by considering a 1:1 aspect ratio square-shaped area, the value of which is derived from the dimension (in pixel-size) of the viewed image having the smaller numerical value (whether that may be the vertical, or the horizontal, dimension in units of pixels).
Viewing from a (viewer to monitor/display) distance that is farther away than "up-close" will "improve" matters (by reducing the lack of detail that the viewer will notice in the image, due to the characteristics of human vision). No "fudge-factors" are applied to modify the DOF result for the viewing of a particular (physical) display/printed size at some particular viewing distance, or to take into account potential non-ideal (non 20/20) human vision.
I have found that my program appears to correspond pretty well with the results that I get from applying it with my Panasonic cameras. I notice (as well) - at least in the case of the DMC-LX3 - that it gives "conservative" (somewhat smaller) DOF values than does the on-line calculator at:
http://www.dofmaster.com/dofjs.html
However (as I have noted above in this thread), the DOF Master database for the "Circle of Confusion" (COC) for various cameras only provides values that fall on integer values of Micrometers, and (particularly when the sensor to subject distance approaches the Hyperfocal Distance), these "rounding errors" can contribute significantly to errors in the calculation of DOF. So, perhaps that is what is going on ... If so, this "rounding error" may well result in random variations from the actual DOF that the DOF Master on-line calculator derives for various brands/models of cameras. These errors are not significant in the case of macro distances, and have only moderate effects upon the "DOF = D" calculations listed below. The largest effect of these errors will be on the value of the Hyperfocal Distance itself (directly proportional to the amount of the error in the COC dimension used). The DOF for sensor to subject distances that are approaching the Hyperfocal Distance amplify these errors considerably (such that the calculated value of the DOF can be in error by many multiples of the more precise value derived from a non-rounded COC).
I had to modify the code in my program to input/output metric units, and iterating with calculations took me a while - so I stuck with just doing the numbers numbers for the (stock) 5.9mm (full wide-angle, actual) focal length of your GRD II, and also using with 5.52 mm height of the image-sensor active-area numerical value that you provided for your (GRD II) image-sensor.
Another reason that I chose not to perform an entire second set of numbers for the 4.40 mm focal length figure that you provided is that (I assume) that this is for an add-on lens. I don't know very much about optics - so I am not sure whether the (above described) "symmetrical lens" condition continues to hold in the case of add-on lenses that provide additional magnification. Maybe some person with a deeper understanding than my own will read the source material from which my calculating code was derived at:
http://www.largeformatphotography.info/ ... nDepth.pdf
and render their expert opinion on whether such remains the case.
The GRD III is very similar to the GRD II. The GRD III has a 6.0 mm focal length, and a 1/1.70 Inch (rather than 1/1.75 Inch) total diagonal dimension of it's (entire) image-sensor assembly. Thus, these results listed below should be reasonably valid for the GRD III, as well.
All distances listed below are in Meters (or Centimeters, where noted). The F-Numbers used are the exact values based on the powers of 2 (as opposed to the common rounded-off values listed below). The distances describing camera to subject distance ("D" appearing below) are measured from the image-sensor to subject existing on the "focal-plane" that the camera is focused on (as opposed as being from the outer surface of the lens-system to the subject). The "Hyperfocal Distance" ("Dhf" appearing below) is the sensor-subject distance at (and beyond which) the DOF becomes (effectively) "infinite" in numerical value.
For F=2.4
Macro: DOF = 3.0 cm at a sensor-subject distance of 17.5 cm.
DOF=D at 83.8 Centimeters.
Dhf = 2.023 Meters
For F=4.0
Macro: DOF = 3.0 cm at a sensor-subject distance of 13.7 cm.
DOF=D at 50.3 Centimeters.
Dhf = 1.216 Meters
For F=4.5
Macro: DOF = 3.0 cm at a sensor-subject distance of 13.0 cm.
DOF=D at 44.8 Centimeters.
Dhf = 1.085 Meters
For F=5.0
Macro: DOF = 3.0 cm at a sensor-subject distance of 12.2 cm.
DOF=D at 40.5 Centimeters.
Dhf = 0.966 Meters
For F=5.6
Macro: DOF = 3.0 cm at a sensor-subject distance of 11.6 cm.
DOF=D at 34.0 Centimeters.
Dhf = 0.863 Meters
PostScript: I have developed a handy (and easily remembered) "rule of thumb" for Depth of Field for the GRD II and GRD III at an F-Number of 3.2 (a value that will not exceed the diffraction limits, even for a vertical display-size of up to 1200 pixels display height). The estimate is a conservative estimate - the estimated value of the Depth of Field does not exceed the (actual) value of the Depth of Field (DoF).
I used a 1080 vertical display pixel-height to run the calculations that this "rule of thumb" is based upon. This will yield a conservative estimate for those who have 768 pixel-height display screen-size, and conforms to the (more and more common) 1080 pixel- height by 1920 pixel-width of 16:9 aspect-ration wide-screen displays.
At a sensor to focused subject distance of 20 centiMeters, the Depth of Field equals (about) 3.65 cm (a number similar to the number of days in the year). This is about the minimum depth of field that one might want in order to photograph as small 3-dimensional object such as a flower, etc.
As a result of each successive (linear) increase in sensor-subject distance of 20 cm (over and above a distance of 20 cm, and up to 100 cm) the (average) Depth of Field approximately doubles. At distances greater than 100 cm, the DoF begins to increase even more quickly for each 20 cm increase in sensor-subject distance, until it reaches "infinity" at the Hyperfocal Distance of 2.15 Meters.
Mathematically, this can be expressed as:
DoF = (3.65) * ( (2)^(cm/20) ) [in units of centiMeters]
where "cm" is the sensor-subject distance.
A look-up table of approximate DoF values (for sensor-subject distances between 20 cm and 100 cm):
At 20 cm, the DoF = 3.65 cm
At 40 cm, the DoF = 14.6 cm
At 60 cm, the DoF = 29.2 cm
At 80 cm, the DoF = 58.4 cm
At 100 cm, the DoF = 117 cm
Happy snappin' ...
These are results for your 768 pixel-height display screen-size. A caveat. While this may seem counter-intuitive - the Depth of Field (DOF) actually decreases with increasing monitor/display screen-sizes (in pixels). Keep that in mind if you are considering full-sized (or slightly cropped) images out of camera, or as they are previewed in a ("raw", TIF, or JPG) post-processor, or if you are producing final JPGs for display that are larger than 1024x768 ...
This is the "object-space" DOF for a symmetrical lens. The multiple lens-systems in our cameras (as I understand it) approximate that condition. As an "object-space" calculation, it assumes the "worst-case scenario" - that the viewer is viewing the monitor/display (whatever it's physical size may be), "up-close".
It is not important whether the viewed 768 pixel-height image fills the entire monitor/display screen, or just fills a portion of the monitor/display screen's size (in pixels). It is not important how physically large the monitor/display screen is. Since it is assumed that the viewer is "up-close", all that matters is that the viewed image is 768 pixels in height. It does not matter whether the horizontal pixel-size of the image is 1024 pixels (or more than 1024 pixels). The Depth of Field is derived by considering a 1:1 aspect ratio square-shaped area, the value of which is derived from the dimension (in pixel-size) of the viewed image having the smaller numerical value (whether that may be the vertical, or the horizontal, dimension in units of pixels).
Viewing from a (viewer to monitor/display) distance that is farther away than "up-close" will "improve" matters (by reducing the lack of detail that the viewer will notice in the image, due to the characteristics of human vision). No "fudge-factors" are applied to modify the DOF result for the viewing of a particular (physical) display/printed size at some particular viewing distance, or to take into account potential non-ideal (non 20/20) human vision.
I have found that my program appears to correspond pretty well with the results that I get from applying it with my Panasonic cameras. I notice (as well) - at least in the case of the DMC-LX3 - that it gives "conservative" (somewhat smaller) DOF values than does the on-line calculator at:
http://www.dofmaster.com/dofjs.html
However (as I have noted above in this thread), the DOF Master database for the "Circle of Confusion" (COC) for various cameras only provides values that fall on integer values of Micrometers, and (particularly when the sensor to subject distance approaches the Hyperfocal Distance), these "rounding errors" can contribute significantly to errors in the calculation of DOF. So, perhaps that is what is going on ... If so, this "rounding error" may well result in random variations from the actual DOF that the DOF Master on-line calculator derives for various brands/models of cameras. These errors are not significant in the case of macro distances, and have only moderate effects upon the "DOF = D" calculations listed below. The largest effect of these errors will be on the value of the Hyperfocal Distance itself (directly proportional to the amount of the error in the COC dimension used). The DOF for sensor to subject distances that are approaching the Hyperfocal Distance amplify these errors considerably (such that the calculated value of the DOF can be in error by many multiples of the more precise value derived from a non-rounded COC).
I had to modify the code in my program to input/output metric units, and iterating with calculations took me a while - so I stuck with just doing the numbers numbers for the (stock) 5.9mm (full wide-angle, actual) focal length of your GRD II, and also using with 5.52 mm height of the image-sensor active-area numerical value that you provided for your (GRD II) image-sensor.
Another reason that I chose not to perform an entire second set of numbers for the 4.40 mm focal length figure that you provided is that (I assume) that this is for an add-on lens. I don't know very much about optics - so I am not sure whether the (above described) "symmetrical lens" condition continues to hold in the case of add-on lenses that provide additional magnification. Maybe some person with a deeper understanding than my own will read the source material from which my calculating code was derived at:
http://www.largeformatphotography.info/ ... nDepth.pdf
and render their expert opinion on whether such remains the case.
The GRD III is very similar to the GRD II. The GRD III has a 6.0 mm focal length, and a 1/1.70 Inch (rather than 1/1.75 Inch) total diagonal dimension of it's (entire) image-sensor assembly. Thus, these results listed below should be reasonably valid for the GRD III, as well.
All distances listed below are in Meters (or Centimeters, where noted). The F-Numbers used are the exact values based on the powers of 2 (as opposed to the common rounded-off values listed below). The distances describing camera to subject distance ("D" appearing below) are measured from the image-sensor to subject existing on the "focal-plane" that the camera is focused on (as opposed as being from the outer surface of the lens-system to the subject). The "Hyperfocal Distance" ("Dhf" appearing below) is the sensor-subject distance at (and beyond which) the DOF becomes (effectively) "infinite" in numerical value.
For F=2.4
Macro: DOF = 3.0 cm at a sensor-subject distance of 17.5 cm.
DOF=D at 83.8 Centimeters.
Dhf = 2.023 Meters
For F=4.0
Macro: DOF = 3.0 cm at a sensor-subject distance of 13.7 cm.
DOF=D at 50.3 Centimeters.
Dhf = 1.216 Meters
For F=4.5
Macro: DOF = 3.0 cm at a sensor-subject distance of 13.0 cm.
DOF=D at 44.8 Centimeters.
Dhf = 1.085 Meters
For F=5.0
Macro: DOF = 3.0 cm at a sensor-subject distance of 12.2 cm.
DOF=D at 40.5 Centimeters.
Dhf = 0.966 Meters
For F=5.6
Macro: DOF = 3.0 cm at a sensor-subject distance of 11.6 cm.
DOF=D at 34.0 Centimeters.
Dhf = 0.863 Meters
PostScript: I have developed a handy (and easily remembered) "rule of thumb" for Depth of Field for the GRD II and GRD III at an F-Number of 3.2 (a value that will not exceed the diffraction limits, even for a vertical display-size of up to 1200 pixels display height). The estimate is a conservative estimate - the estimated value of the Depth of Field does not exceed the (actual) value of the Depth of Field (DoF).
I used a 1080 vertical display pixel-height to run the calculations that this "rule of thumb" is based upon. This will yield a conservative estimate for those who have 768 pixel-height display screen-size, and conforms to the (more and more common) 1080 pixel- height by 1920 pixel-width of 16:9 aspect-ration wide-screen displays.
At a sensor to focused subject distance of 20 centiMeters, the Depth of Field equals (about) 3.65 cm (a number similar to the number of days in the year). This is about the minimum depth of field that one might want in order to photograph as small 3-dimensional object such as a flower, etc.
As a result of each successive (linear) increase in sensor-subject distance of 20 cm (over and above a distance of 20 cm, and up to 100 cm) the (average) Depth of Field approximately doubles. At distances greater than 100 cm, the DoF begins to increase even more quickly for each 20 cm increase in sensor-subject distance, until it reaches "infinity" at the Hyperfocal Distance of 2.15 Meters.
Mathematically, this can be expressed as:
DoF = (3.65) * ( (2)^(cm/20) ) [in units of centiMeters]
where "cm" is the sensor-subject distance.
A look-up table of approximate DoF values (for sensor-subject distances between 20 cm and 100 cm):
At 20 cm, the DoF = 3.65 cm
At 40 cm, the DoF = 14.6 cm
At 60 cm, the DoF = 29.2 cm
At 80 cm, the DoF = 58.4 cm
At 100 cm, the DoF = 117 cm
Happy snappin' ...
Detail Man
New Member
Correction: Depth of Field Data for GRD II and GRD III
NOTICE: The numerical results (in the post directly above this post) are corrected (got it right the 2nd time) - and are significantly more positive (about the same as the Panasonic DMC-LX3).
I tried to modify my program code for Metric - must have missed one detail ... :geek: Went back to my original (proven) program code, and just did the "English"/Metric conversions manually.
Such is life in the "nerd-lane" ...
NOTICE: The numerical results (in the post directly above this post) are corrected (got it right the 2nd time) - and are significantly more positive (about the same as the Panasonic DMC-LX3).
I tried to modify my program code for Metric - must have missed one detail ... :geek: Went back to my original (proven) program code, and just did the "English"/Metric conversions manually.
Such is life in the "nerd-lane" ...
Detail Man
New Member
GRD II and GRD III Diffraction Limited Aperture
From the information in this thread's post:
viewtopic.php?f=34&t=3784#p16152
The GRD II and GRD III image sensors both have an active-height of (about) 5.52 mm.
At a 2736 Pixel height (10 Mpixel mode; 4:3 Aspect Ratio), the "pixel-pitch" (distance between pixels) = (5.52 mm) / 2736 = (approximately) 2 microMeters.
To determine the diffraction limited aperture, define the lower-limit of the Circle of Confusion (COC) as 2x2 Pixels = 4.0 Micrometers x 4.0 microMeters.
With an active image-sensor height of 5.52 milliMeter, a (minimum assignable) 2-pixel sized COC for this image sensor is valid for screen heights up to 1400 pixels.
The relevant COC for the total camera/display system = (active image-sensor height)/(number of vertical display pixels) = (5.52 mm) / P
[where P is the number of vertical display pixels].
When P = 768 pixels, then COC = 7.188 microMeter;
When P = 1080 pixels, then COC = 5.111 microMeter;
When P = 1200 pixels, then COC = 4.600 microMeter.
The diameter of the "Airy disk" (which is the "blur" effect from diffraction effects at higher F-Numbers) = D = ( 2.44 ) * ( "lamba"; wavelength in Meters) * (F-Number)
which (at the 550 nanoMeter wavelength center of the visible spectrum) yields: D = (1.342 microMeters) * (F-Number)
When the diameter of the "Airy disk" equals the vertical height of the COC, diffraction limited aperture is reached.
This occurs when (1.342 microMeters) * (F-Number) = COC
So, F = (COC) / (1.342 x 10^(-6))
Substituting for COC in the above identity yields:
F = (5.52 x 10^(-3)) / (1.342 x 10^(-6)) / P
Combining factors yields this very close approximation:
Fmax = (4113) / P
So, here is the maximum F-Number from the above three displayed pixel-height values ("P") at which a given image is (actually) displayed:
Fmax = 5.36 [at P=768]
Fmax = 3.81 [at P=1080]
Fmax = 3.43 [at P=1200]
The above post at:
viewtopic.php?f=34&t=3784#p16152
references a source-post indicating that the location of the lens-system "sweet-spot" can (potentially) exist at F-Numbers somewhat greater than the maximum F-Number (Fmax) derived above for diffraction limited aperture effects.
From the information in this thread's post:
viewtopic.php?f=34&t=3784#p16152
The GRD II and GRD III image sensors both have an active-height of (about) 5.52 mm.
At a 2736 Pixel height (10 Mpixel mode; 4:3 Aspect Ratio), the "pixel-pitch" (distance between pixels) = (5.52 mm) / 2736 = (approximately) 2 microMeters.
To determine the diffraction limited aperture, define the lower-limit of the Circle of Confusion (COC) as 2x2 Pixels = 4.0 Micrometers x 4.0 microMeters.
With an active image-sensor height of 5.52 milliMeter, a (minimum assignable) 2-pixel sized COC for this image sensor is valid for screen heights up to 1400 pixels.
The relevant COC for the total camera/display system = (active image-sensor height)/(number of vertical display pixels) = (5.52 mm) / P
[where P is the number of vertical display pixels].
When P = 768 pixels, then COC = 7.188 microMeter;
When P = 1080 pixels, then COC = 5.111 microMeter;
When P = 1200 pixels, then COC = 4.600 microMeter.
The diameter of the "Airy disk" (which is the "blur" effect from diffraction effects at higher F-Numbers) = D = ( 2.44 ) * ( "lamba"; wavelength in Meters) * (F-Number)
which (at the 550 nanoMeter wavelength center of the visible spectrum) yields: D = (1.342 microMeters) * (F-Number)
When the diameter of the "Airy disk" equals the vertical height of the COC, diffraction limited aperture is reached.
This occurs when (1.342 microMeters) * (F-Number) = COC
So, F = (COC) / (1.342 x 10^(-6))
Substituting for COC in the above identity yields:
F = (5.52 x 10^(-3)) / (1.342 x 10^(-6)) / P
Combining factors yields this very close approximation:
Fmax = (4113) / P
So, here is the maximum F-Number from the above three displayed pixel-height values ("P") at which a given image is (actually) displayed:
Fmax = 5.36 [at P=768]
Fmax = 3.81 [at P=1080]
Fmax = 3.43 [at P=1200]
The above post at:
viewtopic.php?f=34&t=3784#p16152
references a source-post indicating that the location of the lens-system "sweet-spot" can (potentially) exist at F-Numbers somewhat greater than the maximum F-Number (Fmax) derived above for diffraction limited aperture effects.