LX3/LX5/LX7 - Sensors and Hyperfocal Distances and Depths of Field

[Detail Man]

DOF is greater by the ratio of the full wide-angle Focal Lengths [5.1mm/4.7mm = 1.0851, 8.51%] when the F-Numbers are equal in the lens-systems of the LX3/LX5 and the LX7. However, note:

Maximum F-Number at 550 nM (GRN): LX3/LX5 F=3.02; LX7 F=2.75 [maximum F-Number -8.94%]

Maximum F-Number at 700 nM (RED): LX3/LX5 F=2.37; LX7 F=2.16 [maximum F-Number -8.86%]

The DOF advantage of the LX7 is only valid below it's maximum F-Numbers listed above. Both cameras are affected by diffraction light-spreading effects from relatively low valued F-Numbers.

The above having been said, even though exceeding the Rayleigh criteria for a 2x2 photo-cell array on these image-sensors does begin a trend of gradually compromised resolution thereafter at higher F-Numbers, the higher DOF system will still retain a (relative, in this case small) advantage in terms of the Depth of the Field of focus - while diffraction will degrade the overall resolution within that Depth of Field of focus. A pinhole camera has very high DOF, but also has lots of diffraction ...

Here is a link to an interesting little paper about pinhole cameras, and the difference between high spatial-frequency "resolution" and the "contrast" (which is a predominant factor in the "sharpness")

http://www.biox.kth.se/kjellinternet/Pinhole.pdf

The perception of image "sharpness" is also affected by the characteristics of human visual acuity:

http://www.bobatkins.com/photography/technical/mtf/sqf1.html

 

[ipribadi]

Thanks for the info DM.

That’s quite a low max aperture! But I do understand that it is referring to the onset and grows gradually.

On this subject of DOF and hyperfocal distance, it intrigued me about a year ago on how the contrast detect AF works.

I ended up doing a test on my LX5 and concluded that the contrast detect AF does an approximation of both front and rear limits of the DOF and, for the LX5 at shallow DOF, it chooses a focus distance that is slightly in front of the subject, placing the subject slightly to the rear half of the DOF.

My testing wasn’t scientific in any way and may vary depending on subject distance and DOF, but if true, then assuming a contrast detect AF will set the focus distance exactly at the subject is incorrect. This mainly applies to hyperfocal shooting.

I’ll check to see how the LX7 AF behaves in regards to this.

 

[Detail Man]

Thanks for the info DM.

That’s quite a low max aperture! But I do understand that it is referring to the onset and grows gradually.

On this subject of DOF and hyperfocal distance, it intrigued me about a year ago on how the contrast detect AF works.

I ended up doing a test on my LX5 and concluded that the contrast detect AF does an approximation of both front and rear limits of the DOF ...

Well, since the DOF scales with the viewing-size and viewing-distance, etc. - and is more a matter of a human perceptual judgment-call on what is to the eyes "acceptably sharp" - I don't know if it would be meaningful to choose some arbitrary scaling (of Near and Far Focus distances) in the design of the AF system.

It is true, however, (and I think that this is what you are thinking of), that there are going to be Near and Far distances around the intermediate planes-of-focus chosen within the iterative process where the de-focusing will not contribute useful information to the contrast-detection algorithm.

From the little that I have been able to determine from conversations with kenw (a very sharp EE who posts on the MFTTF sometimes), the iteration process likely tries to converge more quickly by trying to guess where between the early "front-back" end-points the contrast-detection system may generate the highest output-signal (from the highest contrast), as it likely does not have sufficient time to merely hunt-away again and again based on results. This would clearly be a bit of a guess, but (on average) probably still results in reduced iteration-times.

... and, for the LX5 at shallow DOF, it chooses a focus distance that is slightly in front of the subject, placing the subject slightly to the rear half of the DOF.

I don't know about that. Interesting. It seems that, in the final decision between two focus-distances, the algorithm would need to be able to choose between one or the other of the final "guesses" - so maybe they choose the closer of the two ?

My testing wasn’t scientific in any way and may vary depending on subject distance and DOF, but if true, then assuming a contrast detect AF will set the focus distance exactly at the subject is incorrect. This mainly applies to hyperfocal shooting.

Well, there is no absolute exactitude with an iterating servo-system - there is only the "best guess" allowable in the finite time allowed. As we know, the competition for fast AF specs is brutal. To the extent that meeting such specs requires sacrificing the quality of AF, I have always thought that this is a shame - and that cameras should offer two distinct AF modes - one for the "speed freaks" struggling decide quickly on focus, and one for users who are photographing stationary objects (particularly subjects the structure of which has a lot of intricate fine-detail), and who don't mind waiting a tad longer for more reliable results.

Alas, no such thing exists. It's all about "speed", less about "accuracy". That said, the AF system in my GH2 is miles ahead of the one in my LX3 (in temrs of speed, quality, and low-light accuracy).

I’ll check to see how the LX7 AF behaves in regards to this.

Hard stuff to test for. One has to somehow assess accuracy as well as speed (it seems) ...

 

[Detail Man]

I got it (only slightly) wrong on the Circle of Confusion diameters used in previous posts (except for the corrected FZ28 post today) - so I have newly calculated all of the formulas (in units of both Meters as well as Feet) for the LX3/LX5/LX7/FZ50/FZ28/FZ150/FZ200.

These Circle of Confusion diameters are based upon the fairly standard 30 Micron size (for full-frame film/sensors) that the DOF Master (and other) on-line DOF calculators use. These numbers, and the corresponding results are more precise than the DOF Master calculator (because they are not rounded-off to the nearest Micron like the DOF Master COC tables are).

These (standard) formulas are based upon the optical properties of a single symmetrical lens.


.


Hyperfocal Distance and approximate Depth of Field Formulas:

D(hf) is the Hyperfocal Distance

F is the F-Number
Z is the Zoom Factor

D(dof) is the approximate Depth of Field

F is the F-Number
D is the camera-subject distance
Z is the Zoom Factor

Note: Accurate to within less than 11% error when the camera-subject distance is less than 1/3 of the Hyperfocal Distance, and when not shooting very close-up (macro) photography.


.

LX3/LX5 (units of Feet):


D(hf) = ( 12.322 / F ) x ( Z^(2) )


D(dof) ~ ( F / 6.161 ) x ( ( D / Z )^(2) )

LX3/LX5 (units of Meters):

D(hf) = ( 3.756 / F ) x ( Z^(2) )

D(dof) ~ ( F / 1.878 ) x ( ( D / Z )^(2) )

.

LX7 (units of Feet):

D(hf) = ( 11.480 / F ) x ( Z^(2) )

D(dof) ~ ( F / 5.740 ) x ( ( D / Z )^(2) )

LX7 (units of Meters):

D(hf) = ( 3.500 / F ) x ( Z^(2) )

D(dof) ~ ( F / 1.750 ) x ( ( D / Z )^(2) )

.

FZ50 (units of Feet):

D(hf) = ( 32.980 / F ) x ( Z^(2) )

D(dof) ~ ( F / 16.490 ) x ( ( D / Z )^(2) )

FZ50 (units of Meters):

D(hf) = ( 10.052 / F ) x ( Z^(2) )

D(dof) ~ ( F / 5.026 ) x ( ( D / Z )^(2) )

.



FZ28 (units of Feet):



D(hf) = ( 13.262 / F ) x ( Z^(2) )



D(dof) ~ ( F / 6.631 ) x ( ( D / Z )^(2) )



FZ28 (units of Meters):



D(hf) = ( 4.042 / F ) x ( Z^(2) )



D(dof) ~ ( F / 2.021 ) x ( ( D / Z )^(2) )

.



FZ150 (units of Feet):



D(hf) = ( 11.681 / F ) x ( Z^(2) )



D(dof) ~ ( F / 5.841 ) x ( ( D / Z )^(2) )



FZ150 (units of Meters):



D(hf) = ( 3.560 / F ) x ( Z^(2) )



D(dof) ~ ( F / 1.780 ) x ( ( D / Z )^(2) )

.



FZ200 (units of Feet):



D(hf) = ( 11.656 / F ) x ( Z^(2) )



D(dof) ~ ( F / 5.828 ) x ( ( D / Z )^(2) )



FZ200 (units of Meters):



D(hf) = ( 3.553 / F ) x ( Z^(2) )



D(dof) ~ ( F / 1.776 ) x ( ( D / Z )^(2) )

.

DM ...

 

[Detail Man]

There is a somewhat less mathematically complicated approach than the Hyperfocal Distance and Depth of Field formulas. It is format-independent (it is not dependent at all upon image-sensor size), and thus it does not require the calculation of a Circle of Confusion diameter.

This is quite handy, because the Circle of Confusion diameter is inversely proportional to changes in the viewing-size, and is directly proportional to changes in the viewing-distance. The "standard" Circle of Confusion diameter is based uon an 8"x10" viewing-size viewed at a 25cm viewing-distance with ideal human visual acuity (but has to be scaled by viewing size and distance).


The Circle of Confusion (as it is referenced to the surface of the film/sensor, or to the surface of the viewed image) is replaced by a "Disk of Confusion" which represents the actual size of a resolvable disk in "object space" (which just means in the subject-matter being photographed).

From Merklinger's Figure 2 at:

http://www.trenholm.org/hmmerk/DOFR.html


... the following Near and Far Focus distances can be derived:


Dn = (D) x ( 1 - ( (S) (F) / (L) ) )

Df = (D) x ( 1 + ( (S) (F) / (L) ) )

where:

Dn is the Near Focus Distance;
Df is the Far Focus Distance;
D is the Camera to Subject Distance (from lens front nodal-plane to plane-of-focus);
S is the object-field Spot Size as specified by photographer (the "Disk of Confusion");
F is the F-Number;
L is the actual Focal Length.

Calculating the difference between Df and Dn (above) yields a quantity similar to Depth of Field:

(Df - Dn) = (2) x (D) x (S) x (F) / (L)

Note: When the camera's lens-system is focused at "infinity", the Near Focus Distance turns out to be equal to the Hyperfocal Distance as calculated using the "standard method".

 

[Detail Man]

Detail Man wrote:

There is a somewhat less mathematically complicated approach than the Hyperfocal Distance and Depth of Field formulas. It is format-independent (it is not dependent at all upon image-sensor size), and thus it does not require the calculation of a Circle of Confusion diameter.

This is quite handy, because the Circle of Confusion diameter is inversely proportional to changes in the viewing-size, and is directly proportional to changes in the viewing-distance. The "standard" Circle of Confusion diameter is based uon an 8"x10" viewing-size viewed at a 25cm viewing-distance with ideal human visual acuity (but has to be scaled by viewing size and distance).


The Circle of Confusion (as it is referenced to the surface of the film/sensor, or to the surface of the viewed image) is replaced by a "Disk of Confusion" which represents the actual size of a resolvable disk in "object space" (which just means in the subject-matter being photographed).

From Merklinger's Figure 2 at:

http://www.trenholm.org/hmmerk/DOFR.html


... the following Near and Far Focus distances can be derived:


Dn = (D) x ( 1 - ( (S) (F) / (L) ) )

Df = (D) x ( 1 + ( (S) (F) / (L) ) )

where:

Dn is the Near Focus Distance;
Df is the Far Focus Distance;
D is the Camera to Subject Distance (from lens front nodal-plane to plane-of-focus);
S is the object-field Spot Size as specified by photographer (the "Disk of Confusion");
F is the F-Number;
L is the actual Focal Length.

Calculating the difference between Df and Dn (above) yields a quantity similar to Depth of Field:

(Df - Dn) = (2) x (D) x (S) x (F) / (L)

Let's rename (Df - Dn) to Depth of Field (DOF) for the sake of simplicity in notation.


Re-arranging to solve for the (dimensionless) ratio of the width of focus divided by the distance:

( DOF ) / ( D ) = ( 2 ) x ( F ) x ( S ) / ( L )

Substituting Z x L for L (where Z is the Zoom Factor of the lens-system):

( DOF ) / ( D ) = ( 2 ) x ( F ) x ( S ) / ( ( Z ) x ( L ) )


Set the Spot Size (S) equal to values between 0.45mm and 0.51mm (especially handy numbers to use) and combine values to yield:

( DOF ) / ( D ) = ( F ) / ( ( 5 ) x ( Z ) )

Divide both sides by a factor of two to yield:

( ( DOF ) / (2) ) / ( D ) = ( F ) / ( ( 10 ) x ( Z ) )

Invert both sides of the equation, and this formula nicely simplifies to:

( D ) / ( Depth of Field / 2 ) = ( 10 ) x ( Zoom Factor ) / ( F-Number )

where D is the Camera to Subject Distance (from lens front nodal-plane to plane-of-focus).

With Merklinger's DOF, the distance between the Plane of Focus and the Near Focus Distance, and the distance between the Plane of Focus and the Far Focus Distance are always equal. Furthermore, the relationships are independent of the particular sensor-size. Merklinger's DOF is a lot easier to think about, and to apply, than the "standard" DOF formulas. No COC diameter that changes with viewing-size or changes with viewing-distance. No fuss, no buss ! ...


.

SUMMARY (the specific procedure to use described):

(1) Focus on a subject at any distance (D) from the camera. DOF/2 is the distance behind the distance (D) that you want to be in-focus. DOF/2 is also the distance in front of distance (D) that you want to be in-focus. These two distances (around the Plane of Focus) will be equal.


(2) Estimate the numerical ratio of the Camera to Subject Distance (D) divided by DOF/2 that you want to be in focus (both behind, as well as in front, of the Plane of Focus). That ratio needs to have a numerical value that is equal to (or more typically greater than) one (1.0).


(3) Multiply the Zoom Factor displayed by the cameras by a factor of 10.

(4) Adjust the F-Number to a value that when divided into 10 times the Zoom Factor is equal to (or greater than) the numerical ratio estimated in Step (2) above.

.


The numerical formula for the above described procedure is:

( D ) / ( Depth of Field / 2 ) = ( 10 ) x ( Zoom Factor ) / ( F-Number )

where D is the Camera to Subject Distance (from lens front nodal-plane to plane-of-focus).

.

Real World Example of the Numerical Calculations (this is easier than you may think):

(1) You focus on a subject that exists approximately 1.0 Meter (100cm) away from camera.

You would like the Depth of Field around the subject to extend 0.25 Meters (25cm) behind the subject focused-on, and to exist 0.25 Meters (25cm) in front of the subject focused-on.


(2) Estimate the ratio between the 1.0 Meter subject-distance (D) and the in-focus distances (existing behind, as well as in front of, the subject focused-on). That ratio is the number four (4.0).

(3) The camera lens-system Zoom Factor indicated in the camera display equals two (2.0). Multiply that number by a factor of ten (10). The result is twenty (20).

(4) The value of the left-side of the equation equals four (4.0) [from Step (2) above].

In order to make the numerical value of the right side of the equation equal the value of the left side of the equation (which equals 4.0), it is necessary to to divide the value of the right side of the equation [which is presently twenty (20), from Step (3) above] by a factor of five (5.0).

Set the value of the F-Number to a value of five (5.0). The equation balances. You are done ! ...

Note: Of course, higher F-Numbers require slower Shutter Speeds and/ot higher ISO Gains.

 

[Detail Man]

Detail Man wrote:
SUMMARY (the specific procedure to use described):
(1) Focus on a subject at any distance (D) from the camera. DOF/2 is the distance behind the distance (D) that you want to be in-focus. DOF/2 is also the distance in front of distance (D) that you want to be in-focus. These two distances (around the Plane of Focus) will be equal.


(2) Estimate the numerical ratio of the Camera to Subject Distance (D) divided by DOF/2 that you want to be in focus (both behind, as well as in front, of the Plane of Focus). That ratio needs to have a numerical value that is equal to (or more typically greater than) one (1.0).


(3) Multiply the Zoom Factor displayed by the cameras by a factor of 10.

(4) Adjust the F-Number to a value that when divided into 10 times the Zoom Factor is equal to (or greater than) the numerical ratio estimated in Step (2) above.

.


The numerical formula for the above described procedure is:

( D ) / ( Depth of Field / 2 ) = ( 10 ) x ( Zoom Factor ) / ( F-Number )

where D is the Camera to Subject Distance (from lens front nodal-plane to plane-of-focus).

.

Real World Example of the Numerical Calculations (this is easier than you may think):

(1) You focus on a subject that exists approximately 1.0 Meter (100cm) away from camera.

You would like the Depth of Field around the subject to extend 0.25 Meters (25cm) behind the subject focused-on, and to exist 0.25 Meters (25cm) in front of the subject focused-on.


(2) Estimate the ratio between the 1.0 Meter subject-distance (D) and the in-focus distances (existing behind, as well as in front of, the subject focused-on). That ratio is the number four (4.0).

(3) The camera lens-system Zoom Factor indicated in the camera display equals two (2.0). Multiply that number by a factor of ten (10). The result is twenty (20).

(4) The value of the left-side of the equation equals four (4.0) [from Step (2) above].

In order to make the numerical value of the right side of the equation equal the value of the left side of the equation (which equals 4.0), it is necessary to to divide the value of the right side of the equation [which is presently twenty (20), from Step (3) above] by a factor of five (5.0).

Set the value of the F-Number to a value of five (5.0). The equation balances. You are done !

Note: Of course, higher F-Numbers require slower Shutter Speeds and/or higher ISO Gains.

Unfortunately, Panasonic cameras only display the Zoom Factor with a resolution of zero digits to the right of the decimal-point. This means that one could conceivably be adjusted to have a Zoom Factor of (for instance) 1.99 - and the display would only indicate Zoom Factor = 1.0.

This can lead to computational errors due to the limited resolution of the Zoom Factor display.


The best thing that one can do to attempt to reduce these errors is to try to be aware of the (approximate) Zoom Factor that has been adusted to using the Zoom control. If your best guess (in example) is that the Zoom Factor is in the range of 1.5, then round-up the value used in the above procedure to the next higher integer value (2.0 in this case), and use that (mentally) rounded-up integer Zoom Factor value (instead of what the camera is displaying).

Doing this will help to ensure that the camera system will provide (at least) the desired DOF.

 

[teddoman]

If pixel pitch is the same as pixel diameter, and is 1.846 microns for the LX7, is there a consensus on the LX7's diffraction limit?

Cambridgeincolour seems to think "an airy disk can have a diameter of about 2-3 pixels before diffraction limits resolution". 2-3 pixels is not very firm guidance, as that's the difference between an airy disk of 3.7 and 5.5 microns (using CIC's visual example), or somewhere between f/2.8-f/4. Is it possible diffraction limits set in so early for the LX7?

If so, where should I be trying to stop to avoid diffraction, at f/2.8 or at f/4?

Detail Man wrote:

Had not realized that the LX7 has a somewhat smaller sensor than the LX3 and LX5 so I had a look:

http://www.dpreview.com/previews/panasonic-lumix-dmc-lx7

From that information (and Panasonic's statement that the LX3/LX5 image-sensor pixel-pitch equals 2.025 Microns), I derived the following information (sensor dimensions for 4:3 aspect-ratio mode):

LX3/LX5

Pixel-pitch=2.025 Microns. Active sensor dimensions are 7.3872mm x 5.5404mm. Active sensor area=40.9280mm. Minimum Focal Length=5.1mm. Circle of Confusion diameter=6.403 Microns (based on 30 Micron full-frame COC diameter, 8"x10" size viewed at 25cm with 20/20 visual acuity)

Hyperfocal Distance [HFD in Meters] = ( 4.062 ) x ( Z^(2) ) / ( F )

Hyperfocal Distance [HFD in Feet] = ( 13.328 ) x ( Z^(2) ) / ( F )

where:
Z is Zoom Factor;
F is F-Number.
.

LX7

Pixel-pitch=1.846 Microns. Active sensor dimensions are 6.7342mm x 5.0507mm. Active sensor area=34.0124mm. Minimum Focal Length=4.7mm. Circle of Confusion diameter=5.837 Microns (based on 30 Micron full-frame COC diameter, 8"x10" size viewed at 25cm with 20/20 visual acuity)

Hyperfocal Distance [in Meters] = ( 3.785 ) x ( Z^(2) ) / ( F )

Hyperfocal Distance [in Feet] = ( 12.417 ) x ( Z^(2) ) / ( F )

where:
Z is Zoom Factor;
F is F-Number.
.

Note: The formulas for Hyperfocal Distance above are very close approximations when the Camera-Subject Distance (between the front nodal-plane of the lens-system and the plane-of-focus) is significantly larger than the (actual) Focal Length multiplied by Zoom Factor. This is true in all but the very closest-up of of shooting conditions - so they can be considered to be accurate .
.

Calculating the Depth of Field from the Hyperfocal Distance

Units of either Meters or Feet can be used (as long as the same units are used when entering HFD and D ). HFD is the Hyperfocal Distance (calculated from the above formulas). D is the Camera-Subject Distance (between the front nodal-plane of the lens-system and the plane-of-focus).

An approximation valid (with not more than 11% error) when D is equal to or less than 1/3 of HFD

Depth of Field [DOF] ~ ( 2 ) x ( D^(2) ) / ( HFD )

A precise formula valid when D has a value less than the HFD ( undefined when D => the HFD ):

Depth of Field [DOF] = ( 2 ) x ( D ) / ( ( HFD / D ) - ( D / HFD ) )

 

[Detail Man]

tedandtricia wrote:

If pixel pitch is the same as pixel diameter, and is 1.846 microns for the LX7, is there a consensus on the LX7's diffraction limit?

In the post below, the dimensions that I worked from for the LX7 active-area do seem to have been correct. DxO Labs rates the LX7 pixel-pitch at 1.96 Microns:

http://www.dxomark.com/index.php/Cameras/Camera-Sensor-Database/Panasonic/Lumix-DMC-LX7

The business of diffraction effects is a murky subject - one that I have been reading and learning about more lately. Here is some information that I hope may aid in understanding.

.

The diameter that they are referring to equals a circle with a diameter that is equal to the linear (height/width) dimensions of 2.43934 photosite apertures (the aperture being the portion of the photosite assembly area that actually contains the photo-sensitive material).

They are referring to the width of the Airy disk main-lobe containing 86% of the total intensity (in units of Watts, or energy in time, per unit area). The other 14% of the total intensity is distributed in decreasing amplitude periodic rings existing farther away from the Airy disk center.

.

Diffraction decreases lens-camera system resolution in a gradual manner - not a "hard and fast" threshold. It is an optical property of the lens. That result then is combined (convolved, mathematically) with the combination response of the AA Filter and photosite aperture.

A good way to think about what happens is in terms of the composite lens-camera system's modulation transfer function (MTF), which is very much like an audio frequency response plot (except the frequencies represents variation of brightness in space, rather than variations of voltage or current or sound pressure level in time).

.

The reference spatial frequency of the system described below corresponds to the reciprocal of the physical dimension of the photosite aperture. For the sake of simplicity, assume that this equals the photo-site dimension (100% Fill Factor). So, the spatial sampling frequency equals the reciprocal of the photosite aperture (which is the same in this case as the photosite-pitch).

What is "hard and fast" is that this system cannot resolve any contrast (will have a modulation transfer function, or MTF, equal to zero response value) when the spatial frequency of the information projected onto the image-sensor equals or exceeds a spatial frequency equal to the reciprocal of the quantity which is the product of the Wavelength multiplied by the F-Number.

The Airy disk main-lobe diameter equals 2.43934 times the product of Wavelength multiplied by the F-Number. It looks like a "blob" that represents the probability of where a photon will end up:

Source: http://upload.wikimedia.org/wikipedia/en/thumb/e/e6/Airy-3d.svg/500px-Airy-3d.svg.png

Typically, the effects of lens-aberrations, de-focussing, and camera movement "swamp" diffraction effects in magnitude, and make for a situation where Airy disk effects cannot be viewed. Nevertheless, the diffraction effects (of light passing through a circular or near-circular aperture) do exist, and they act as a potential limiting factor for camera-lens system resolution.

The BLUE colored plot in the MTF diagram below corresponds to the effects of diffraction only. The RED colored plot shows the effect of the diffraction combined (convolved) together with the photosite. Don't worry about the GREEN colored plot. More information about that here:

http://www.dpreview.com/forums/post/51323729

This is the MTF response plot of a system that does not have an AA Filter attached:


BLUE plot is the diffraction only - RED plot is diffraction combined with Photosite

Unit spatial frequency (1.0 on the X-axis) correspond to the reciprocal of the photosite size. The Wavelength multiplied by F-Number equals the physical dimension of one photosite in size. The physical diameter of the Airy disks correspond to 2.43934 times that single photosite size.

Note that total loss of contrast (MTF=0) occurs only at the highest spatial frequency (the finest detail). If one increases the Wavelength multiplied by F-Number product to a higher value, the spatial frequency (the fine detail) will decrease more and more. However, the effects of diffraction are gradual upon resolution (as opposed to representing a "hard and fast" limit).

.

Things become a little more complex. Any spatial frequency higher than 0.5 (the mid-point of the X-axis) in the diagram above will result in aliasing distortion - so what really matters is the left half of the above diagram only. To see what a realistic camera-lens system looks like, let's pop the strongest possible AA Filter onto that image-sensor. The LX7's may not be quite as strong as the AA Filter below (but it appears to my eyes to be stronger than the LX5's).

Note that the composite system MTF response is more limited by the effects of the photosite combined (convolved) with the AA Filter (the RED colored plot below) than by the diffraction. Increasing the Wavelength multiplied by F-Number product will still degrade lens-camera system resolution gradually - but the net effect of that is less pronounced with the AA Filter added:


With AA Filter - BLUE plot is the diffraction only - RED plot is the composite MTF response

Cambridgeincolour seems to think "an airy disk can have a diameter of about 2-3 pixels before diffraction limits resolution". 2-3 pixels is not very firm guidance, as that's the difference between an airy disk of 3.7 and 5.5 microns (using CIC's visual example), or somewhere between f/2.8-f/4. Is it possible diffraction limits set in so early for the LX7?

If so, where should I be trying to stop to avoid diffraction, at f/2.8 or at f/4?

What matters (at any particular Focal Length) is where the increasing F-Number ceases to minimize lens-aberrations, and begins to result in a decreasing MTF response. That is best determined via actual MTF tests (as applications like Imatest perform), not by thinking about Airy disks - because the effects of the lens aberrations are unknown, and it is they that determine where that peak MTF ("sweet spot") exists for any given lens-system Focal Length.

DM ...

 

[Detail Man]

Detail Man wrote:

tedandtricia wrote:

If pixel pitch is the same as pixel diameter, and is 1.846 microns for the LX7, is there a consensus on the LX7's diffraction limit?

In the post below, the dimensions that I worked from for the LX7 active-area do seem to have been correct.

SHOULD READ:

In the post below, the dimensions that I worked from for the LX7 active-area do seem to have been incorrect.

DxO Labs rates the LX7 pixel-pitch at 1.96 Microns:

http://www.dxomark.com/index.php/Cameras/Camera-Sensor-Database/Panasonic/Lumix-DMC-LX7

 

[Detail Man]

Detail Man wrote:
The diameter that they are referring to equals a circle with a diameter that is equal to the linear (height/width) dimensions of 2.43934 photosite apertures (the aperture being the portion of the photosite assembly area that actually contains the photo-sensitive material).
They are referring to the width of the Airy disk main-lobe containing 86% of the total intensity (in units of Watts, or energy in time, per unit area). The other 14% of the total intensity is distributed in decreasing amplitude periodic rings existing farther away from the Airy disk center.
The Airy disk main-lobe diameter equals 2.43934 times the product of Wavelength multiplied by the F-Number. It looks like a "blob" that represents the probabilityof where a photon will end up:

Source: http://upload.wikimedia.org/wikipedia/en/thumb/e/e6/Airy-3d.svg/500px-Airy-3d.svg.png

Typically, the effects of lens-aberrations, de-focussing, and camera movement "swamp" diffraction effects in magnitude, and make for a situation where Airy disk effects cannot be viewed. Nevertheless, the diffraction effects (of light passing through a circular or near-circular aperture) do exist, and they act as a potential limiting factor for camera-lens system resolution.

Cambridgeincolour seems to think "an airy disk can have a diameter of about 2-3 pixels before diffraction limits resolution". 2-3 pixels is not very firm guidance, as that's the difference between an airy disk of 3.7 and 5.5 microns (using CIC's visual example), or somewhere between f/2.8-f/4. Is it possible diffraction limits set in so early for the LX7?

If so, where should I be trying to stop to avoid diffraction, at f/2.8 or at f/4?

What matters (at any particular Focal Length) is where the increasing F-Number ceases to minimize lens-aberrations, and begins to result in a decreasing MTF response. That is best determined via actual MTF tests (as applications like Imatest perform), not by thinking about Airy disks - because the effects of the lens aberrations are unknown, and it is they that determine where that peak MTF ("sweet spot") exists for any given lens-system Focal Length.

Something that I did not mention is that on a Bayer-arrayed image-sensor, the RGBG color filtered photosites fill a 2x2 photosite area. All but the most very rudimentary de-mosaicing algorithms take more than a 2x2 photosite area into account when rendering single pixels in a RGB color-space.

So, 1x1 photosite analysis only really makes sense for a monochromatic image-sensor, and (as a result of these larger photosite dimensions described), and Airy disk main-lobe diameter of 2.43934 photosites is probably no larger than the (actual) relevant "minimum photosite area" from which pixels are rendered by de-mosaicing into a RGB color space.

Once again (even on the level of 1x1 photosite analysis), the effects of the AA Filter and photosite aperture on composite system MTF response tend to be more significant than the effects of diffraction. Diffraction resolution losses still matter - but with a reduced adjustment sensitivity.

Further, just because the MTF response is reduced at the highest spatial frequencies, one may value and truly need the DOF gained from increasing the F-Number, and sharpening (via subtractive or deconvolution filtering sharpening processes) can to some extent compensate for reduced MTF response (up to a point, though signal/noise ratio will be reduced as a result).

When shooting up-close, when one really needs the DOF, probably better to not worry very much about diffraction. When shooting subject-matter at a distance (where the subject-matter of interest will be projected onto a limited number of image-sensor photosites), DOF is seldom as significant of a problem, and the F-Number can then be limited to the "sweet spot" where the softening effects of lens-aberrations are no longer decreased by increasing the F-Number.

For what it is worth, DIWA tests using DxOMark testing equipment found the LX3 lens-system to (at wide-angle) have the highest MTF(50%) at F=2.8 and the lowest Lens-blur (in BxU) at F=4.0. At full telephoto, the highest MTF(50%) is at F=4.0 and the lowest Lens-blur (in BxU) at F=5.6. Unfortunately DIWA labs folded before being able to test the LX5 lens-system.

 

[LeRentier]

Detail Man wrote:

Twan Van Dommelen wrote:

... and your point is...?

Interesting mathematics, and im not sure i can follow youi. But im trying to understand your point.

When the Camera-Subject Distance ( D ) equals the Hyperfocal Distance ( HFD ), then everything from one-half (1/2) of the Hyperfocal Distance (in front of the plane-of-focus, where the focused-on subject exists), to "infinity" (behind the plane-of-focus, where the focused-on subject exists) will be in focus. The distance between those two locations (the Near Focus Distance and the Far Focus Distance) is called the Depth of Field ( DOF ). However, no lens-system is perfect ...

Another valid approach (Merklinger) is to focus on the far-field to ensure the best far-field focus.

Sounds nice but, how do you set the hyperfocal distance on a compact ?

 

[Detail Man]

LeRentier wrote:

Detail Man wrote:

Twan Van Dommelen wrote:

... and your point is...?

Interesting mathematics, and im not sure i can follow youi. But im trying to understand your point.

When the Camera-Subject Distance ( D ) equals the Hyperfocal Distance ( HFD ), then everything from one-half (1/2) of the Hyperfocal Distance (in front of the plane-of-focus, where the focused-on subject exists), to "infinity" (behind the plane-of-focus, where the focused-on subject exists) will be in focus. The distance between those two locations (the Near Focus Distance and the Far Focus Distance) is called the Depth of Field ( DOF ). However, no lens-system is perfect ...

Another valid approach (Merklinger) is to focus on the far-field to ensure the best far-field focus.

Sounds nice but, how do you set the hyperfocal distance on a compact ?

By increasing the F-Number (in Aperture Priority mode) to decrease the Hyperfocal Distance (making the Depth of Field, DOF deeper), or by increasing the Zoom Factor to increase the Hyperfocal Distance (making the DOF shallower).

Use these (revised) formulas posted on this thread for a number of Panasonic compacts (all of which have Aperture Priority mode options) to estimate the Hyperfocal Distance and/or the DOF:

http://www.dpreview.com/forums/post/50136412

Adjusting the F-Number does not change the Field of View, and can be done in 1/3 stop increments. Hyperfocal Distance and DOF change in direct proportion to the change in F-Number.

Adjusting Zoom Factor changes the Field of View (which the user wants to set to achieve desired framing of the image, as opposed to the Hyperfocal Distance and DOF), and the only way that the user can see what the Zoom Factor is is on the preview-screen/EVF displays, where it is only displayed with one digit precision (no digits to the right of the decimal point at all).

Using more Zoom always increase the Hyperfocal Distance larger (making the DOF shallower). The effect is very pronounced (changes are in proportion to the square of the change in Zoom Factor).

The best approach is to setting whatever framing one wants by adjusting the Zoom Factor, focus on what you want to be in the very best focus, then adjust the F-Number for the desired DOF.

 

[Samuel Dilworth]

The LX7 has a pixel pitch of 1.85 µm according to this PDF (from Sony, the sensor manufacturer). DxO Labs frequently gets the camera details wrong. The LX3 and LX5 have a pixel pitch of 2.025 µm (stated here, for example).

Comparing the size of the Airy disc to the pixel pitch to come up with a supposed diffraction-limited f-number is not a useful thing to do. What matters, as Detail Man notes, is where the lens aberrations (which improve upon stopping down, but are always present) are optimally balanced against diffraction (which gets worse upon stopping down, but is always present – even at f/2).

Therefore the optimum f-number for sharpness depends to a great extent on the aberrations in the lens. Lens aberrations vary hugely depending on the focal length (zoom setting) and where you’re looking in the frame – the centre, the edge, the very corner?

The result is that best sharpness (system MTF) might be at f/2.5 in the centre and f/5.6 in the extreme corners, no matter how horrifyingly large the Airy disc is at f/5.6 on an LX-series camera.

And as Detail Man also notes, if you need the depth of field of a small aperture then you need the depth of field. Any quibbling about the optimum aperture for sharpness won’t matter if your subject is blatantly out of focus!

 

[Detail Man]

Samuel Dilworth wrote:

The LX7 has a pixel pitch of 1.85 µm according to this PDF (from Sony, the sensor manufacturer). DxO Labs frequently gets the camera details wrong. The LX3 and LX5 have a pixel pitch of 2.025 µm (stated here, for example).

Comparing the size of the Airy disc to the pixel pitch to come up with a supposed diffraction-limited f-number is not a useful thing to do. What matters, as Detail Man notes, is where the lens aberrations (which improve upon stopping down, but are always present) are optimally balanced against diffraction (which gets worse upon stopping down, but is always present – even at f/2).

Therefore the optimum f-number for sharpness depends to a great extent on the aberrations in the lens. Lens aberrations vary hugely depending on the focal length (zoom setting) and where you’re looking in the frame – the centre, the edge, the very corner?

The result is that best sharpness (system MTF) might be at f/2.5 in the centre and f/5.6 in the extreme corners, no matter how horrifyingly large the Airy disc is at f/5.6 on an LX-series camera.

And as Detail Man also notes, if you need the depth of field of a small aperture then you need the depth of field. Any quibbling about the optimum aperture for sharpness won’t matter if your subject is blatantly out of focus!

Thanks for providing the link to the Sony document identifying the LX7 image-sensor as Sony Exmor back-lit item. Have seen some speculation as to the sensor being back-lit, but nothing seemingly solid previously. Guess that I got the pixel-pitch about right in the first place. Yes, DxOMark pixel-pitch information has been incorrect before (Olympus XZ-1 data at one point, until subsequently corrected). One would think that they could do a better job at that data.

 

[teddoman]

Detail Man wrote:

Samuel Dilworth wrote:

The LX7 has a pixel pitch of 1.85 µm according to this PDF (from Sony, the sensor manufacturer). DxO Labs frequently gets the camera details wrong. The LX3 and LX5 have a pixel pitch of 2.025 µm (stated here, for example).

Comparing the size of the Airy disc to the pixel pitch to come up with a supposed diffraction-limited f-number is not a useful thing to do. What matters, as Detail Man notes, is where the lens aberrations (which improve upon stopping down, but are always present) are optimally balanced against diffraction (which gets worse upon stopping down, but is always present – even at f/2).

Therefore the optimum f-number for sharpness depends to a great extent on the aberrations in the lens. Lens aberrations vary hugely depending on the focal length (zoom setting) and where you’re looking in the frame – the centre, the edge, the very corner?

The result is that best sharpness (system MTF) might be at f/2.5 in the centre and f/5.6 in the extreme corners, no matter how horrifyingly large the Airy disc is at f/5.6 on an LX-series camera.

And as Detail Man also notes, if you need the depth of field of a small aperture then you need the depth of field. Any quibbling about the optimum aperture for sharpness won’t matter if your subject is blatantly out of focus!

Thanks for providing the link to the Sony document identifying the LX7 image-sensor as Sony Exmor back-lit item. Have seen some speculation as to the sensor being back-lit, but nothing seemingly solid previously. Guess that I got the pixel-pitch about right in the first place. Yes, DxOMark pixel-pitch information has been incorrect before (Olympus XZ-1 data at one point, until subsequently corrected). One would think that they could do a better job at that data.

Very interesting. I didn't know the LX7 used a Sony sensor. That makes at least two non-Sony cameras I own that use Sony sensors.

I must admit DM's discussion was a bit over my head, as I have not done nearly enough reading on the subject. But generally, it sounds like more lens specific testing of the lens itself would need to be done to determine its diffraction limit, and my understanding is that many of the review websites use this for interchangeable lenses, and come up with 3D analyses of lenses, but I haven't seen this done for lenses on cameras like the LX7 where the zoom lens is affixed to the camera.

 

[morepix]

But why??

 

[Detail Man]

tedandtricia wrote:

Detail Man wrote:

Samuel Dilworth wrote:

The LX7 has a pixel pitch of 1.85 µm according to this PDF (from Sony, the sensor manufacturer). DxO Labs frequently gets the camera details wrong. The LX3 and LX5 have a pixel pitch of 2.025 µm (stated here, for example).

Comparing the size of the Airy disc to the pixel pitch to come up with a supposed diffraction-limited f-number is not a useful thing to do. What matters, as Detail Man notes, is where the lens aberrations (which improve upon stopping down, but are always present) are optimally balanced against diffraction (which gets worse upon stopping down, but is always present – even at f/2).

Therefore the optimum f-number for sharpness depends to a great extent on the aberrations in the lens. Lens aberrations vary hugely depending on the focal length (zoom setting) and where you’re looking in the frame – the centre, the edge, the very corner?

The result is that best sharpness (system MTF) might be at f/2.5 in the centre and f/5.6 in the extreme corners, no matter how horrifyingly large the Airy disc is at f/5.6 on an LX-series camera.

And as Detail Man also notes, if you need the depth of field of a small aperture then you need the depth of field. Any quibbling about the optimum aperture for sharpness won’t matter if your subject is blatantly out of focus!

Thanks for providing the link to the Sony document identifying the LX7 image-sensor as Sony Exmor back-lit item. Have seen some speculation as to the sensor being back-lit, but nothing seemingly solid previously. Guess that I got the pixel-pitch about right in the first place. Yes, DxOMark pixel-pitch information has been incorrect before (Olympus XZ-1 data at one point, until subsequently corrected). One would think that they could do a better job at that data.

Very interesting. I didn't know the LX7 used a Sony sensor. That makes at least two non-Sony cameras I own that use Sony sensors.

I must admit DM's discussion was a bit over my head, as I have not done nearly enough reading on the subject. But generally, it sounds like more lens specific testing of the lens itself would need to be done to determine its diffraction limit, ...

There is no "hard and fast" diffraction "limit". Just gradual resolution decrease after increasing F-Number no longer improves the MTF response (by reducing the affects of lens aberrations).

A guess might be an F-Number equal to double the minimum F-Number at any Focal Length (which will automatically occur when in Aperture Priority shooting mode). That would be F=2.8 at wide-angle and around F=4.5 at full telephoto. If you need more DOF, don't "stop" there ...

... and my understanding is that many of the review websites use this for interchangeable lenses, and come up with 3D analyses of lenses, but I haven't seen this done for lenses on cameras like the LX7 where the zoom lens is affixed to the camera.

For the ideal case of no lens aberrations, assuming a 1.846 Micron photosite aperture (which is larger than it really is, because Fill Factor is not 100%) with a worst-case 700nM wavelength, a F-Number of 2.637 would cause "extinction" at twice the spatial frequency of the Nyquist frequency (where the strongest possible AA Filter would have a zero spatial frequency response). So, where diffraction effects are concernced, it sounds like F=2.8 should be safe in all cases.

However, the existence of lens aberrations may require that you increase the F-Number beyond F=2.8 at Focal Lengths longer than wide-angle in order to achieve the highest possible MTF (which is the relevant goal). Even though some diffraction effects may occur, that does not matter. The higher the MTF response, the "sharper" the image (which is your concern).

DM ...