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

[Detail Man]

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 ) )

 

[Twan Van Dommelen]

... and your point is...?

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

 

[Ray Sachs]

... and your point is...?

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

The LX7 has slightly greater depth of field for a given zoom level and aperture...

I'm the non-detail man...

-Ray
-------------------------
http://www.flickr.com/photos/20889767@N05/collections/72157626204295198/

 

[Detail Man]

... 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.

 

[Twan Van Dommelen]

The LX7 has slightly greater depth of field for a given zoom level and aperture...
I'm the non-detail man...

Ok thanks.
T

 

[Twan Van Dommelen]

@ Detail Man

Thank you for tying to explain.

Greetz
T

 

[Detail Man]

@ Detail Man

Thank you for tying to explain.

You are welcome. If you "google" the phrases "Depth of Field" and "Hyperfocal Distance", you will find many different sources of information about these things. Good concepts to understand !

 

[TanukiSan]

A great site with some more info and information about his,
in a simpler and uderstandable way with the option to do the maths yourself

http://www.dofmaster.com/dofjs.html

 

[Detail Man]

A great site with some more info and information about his,
in a simpler and uderstandable way with the option to do the maths yourself

http://www.dofmaster.com/dofjs.html

Yes, the DOF Master DOF Calculator is one of a number of web-pages that can calculate Depth of Field, Hyperfocal Distance, Near Focus Distance, and Far Focus Distance. There are also other sites.

It uses the same (30 Micron, full-frame) reference Circle of Confusion diameter that I have used in the formulas that I posted. However, the numerical values of the Circle of Confusion diameter that they use are rounded-off (such that the error can approach as much as 20%). Those rounded-off values can lead to errors at higher Camera-Subject distances (as you approach Hyperfocal Distance)

Since our cameras only tell us the "Zoom Factor" when we are using them - reporting Focal Length only later in the image-file meta-data (the "EXIF" data), the formulas that I posted use that Zoom Factor so that they are more directly useful to the user in the field (without doing extra math).

 

[Twan Van Dommelen]

i know what DOF is but i never bothered to try and calculate it. But nevertheless it's interesting to take a look at this.

 

[ipribadi]

The LX7 has slightly greater depth of field for a given zoom level and aperture...

Ray, when you mention "greater" DOF, you mean shallower right?

I just got my LX7 over the weekend.
One thing I tried was comparing the DOF to my LX5.

To me the LX7 DOF is more shallow (me likes!) than the LX5 at all zoom levels, noticable at tele, less noticeable at wide.

 

[Ray Sachs]

The LX7 has slightly greater depth of field for a given zoom level and aperture...

Ray, when you mention "greater" DOF, you mean shallower right?

I just got my LX7 over the weekend.
One thing I tried was comparing the DOF to my LX5.

To me the LX7 DOF is more shallow (me likes!) than the LX5 at all zoom levels, noticable at tele, less noticeable at wide.

No, it should actually be deeper but the qualifier was for a given zoom level and aperture . Since the lens is faster in the LX7, you can get a wider aperture at any zoom level than you could with the LX5, so if you're using the widest possible aperture then, yeah, you should get shallower depth of field. But the impact of the smaller sensor is to give you deeper DOF at a given zoom level and aperture so if you equalize the aperture, I'd think you should have MORE DOF, not less...

Generally, if you're shooting in hyperfocal mode (or zone focus), you're looking for more, rather than less, DOF. If you're looking for less, then you can get it by opening up the aperture all the way, but even with this very fast lens, a compact camera is the wrong place to look for really shallow DOF...

-Ray
-------------------------
http://www.flickr.com/photos/20889767@N05/collections/72157626204295198/

 

[John Miles]

Hey welcome back DM. Can I hijack your thread please, whilst you're here. I am trying to understand the link between sensor size and achievable DOF. You once told me something like for a given DOF sensor size does not deliver a significant advantage; or something along those lines.

As you can see I'm confused, but I would like to understand it more clearly. I know this is a bit rude to ask, but any pointers would be appreciated.
--


The FZ50: DSLR handling of a bright Leica 35-420mm lens that's this good: http://www.flickr.com/groups/panasonicfz50/pool/show (slideshow always good). And now add the LX2: http://www.flickr.com/groups/lx2/pool/show/
[Tomorrows camera is better and smaller than todays]

 

[RedDog Steve]

i know what DOF is but i never bothered to try and calculate it. But nevertheless it's interesting to take a look at this.

Used to be we didn't have to calculate the range, it was clearly marked on the lens for each of the stops.



rd

 

[MustangJoe]

Hi John,

I found these videos quite helpful in understanding how sensor size affects DOF.

First, a refresher on the concept of DOF:

http://www.youtube.com/watch?v=34jkJoN8qOI

Second, an explanation of how your sensor size indirectly affects DOF:

http://www.youtube.com/watch?v=Es7gK3V22hM

Joe
--
http://www.flickr.com/photos/mustangjoe

 

[Detail Man]

Hi John ,

Hey welcome back DM.

I just happened to see something posted that was incorrect last night, and posted to address that, and also ran a few calculations for the LX3/LX5/LX7 Hyperfocal Distances and Depths of Field.

Can I hijack your thread please, whilst you're here.

As you can see I'm confused, but I would like to understand it more clearly. I know this is a bit rude to ask, but any pointers would be appreciated.

I don't mind at all thinking and commenting for friends who are reasonable folks such as yourself.

I am trying to understand the link between sensor size and achievable DOF. You once told me something like for a given DOF sensor size does not deliver a significant advantage; or something along those lines.

What follows assumes a constant Shutter Speed and Camera-Subject Distance, but may involve changes in a camera's ISO Gain (in order to achieve the same overall recorded image-brightness).
.

To record the same image (same Field or Angle of View) with a larger sized image-sensor, the lens Focal Length has to increase in direct proportion for that to be the case. When the F-Number is also increased by that same proportion the DOF will be the same (and Total Light will be the same)

That increased F-Number reduces the Exposure - a function of light-level, T-Number, and Shutter Speed, and not a function of ISO Gain (which only affects overall recorded image-brightness).

Exposure is in units of light per unit area . But, a larger image-sensor has a larger area , so the Total Light transduced by the image-sensor remains the same in the above described situation (of a larger sized image-sensor requiring a longer Focal Length and higher F-Number for the same DOF).
.

In base ISO Gain (or relatively low ISO Gain) applications the dominant noise-source is Photon Shot Noise. It is more significant than the quantization-noise of Analog/Digital Conversion, and is also more significant than Read/Dark Noise is (except in the very deepest shadow-areas of an image).

In the above-described situation, the Signal/Noise Ratio is determined by the amount of Photon Shot Noise (which is a function of the Total Light transduced by the entire image-sensor, and the Quantum Efficiency of the photo-sites). The size (pixel-pitch) of the photo-sites does not matter.

Therefore, two image-sensors of different size (with the same Quantum Efficiency) that exist in camera systems that are adjusted to exhibit the same DOF will have the exhibit Signal/Noise Ratio .

Different image-sensor types do vary somewhat in their Quantum Efficiency (it depends on various factors). The range that they vary over is not that wide, however, and the effect upon image-noise changes only with the square-root of the ratio of the change in Quantum Efficiency.
.

For lower light-level applications (which may involve higher ISO Gains), amplification of the Read/Dark Noise takes place to a greater extent, and, as a result, the Signal/Noise Ratio is determined by the combination (the vector-summation) of the Photon Shot Noise and the Read/Dark Noise (which is always the case, but typically only becomes significant at higher ISO Gains). These two types of noise have an equal contribution to the image-noise at a light-level (in photons) that is equal to the (RMS) Read/Dark Noise squared divided by the Quantum Efficiency.

The amount of Read/Dark Noise that exists in an image-sensor is more complicated than the amount of Photon Shot Noise. It primarily depends a lot on the particular design of the image-sensor (much more so than the size of the individual photo-sites themselves). A complex subject.
.

Summary : Regardless of the Sensor Size, when the Focal Length and the F-Number are adjusted so as to result in the same DOF, the Total Light transduced by the image-sensor is the same. In low ISO Gain applications, the SNR is largely determined by the Photon Shot Noise (which is roughly the same, or at least close in value) which is itself determined by the Total Light (which is the same for the same DOF). In higher ISO Gain applications, the SNR is determined by the combination of Photon Shot Noise and Read/Dark Noise. Depending on the quality of the image-sensor design, more variations may be seen in the SNR as a result of those differences. Thus, in higher ISO Gain applications, only identical image-sensor technologies can be directly compared.

Dynamic Range is affected by an image-sensor's Read/Dark Noise at all ISO Gains, where each doubling in ISO Gain typically reduces sensor's maximum light illumination (saturation) level by two.

DM ...

 

[John Miles]

Fantastic!

I've read it three times now and the grey cell are beginning to quiver. Going back in for another go................

Onward Cristian Soooollllllldierrrss, going as befoooorrrrrre......................

--


The FZ50: DSLR handling of a bright Leica 35-420mm lens that's this good: http://www.flickr.com/groups/panasonicfz50/pool/show (slideshow always good). With the FZ200 performance so good, I live in hope that Mr Ichiro Kitao has triggered the update to the FZ50. http://forums.dpreview.com/forums/read.asp?forum=1033&message=42366095

 

[Detail Man]

Fantastic!

I've read it three times now and the grey cell are beginning to quiver. Going back in for another go................

Onward Cristian Soooollllllldierrrss, going as befoooorrrrrre......................

"Brothers, we are treading where the Saints have trod."

Don't accept any wooden nickels from half-baked posers. There seems to be one behind every tree (here and there). Accept no substitutes. I would not say it unless I knew it to be true ...

 

[ipribadi]

No, it should actually be deeper but the qualifier was for a given zoom level and aperture . Since the lens is faster in the LX7, you can get a wider aperture at any zoom level than you could with the LX5, so if you're using the widest possible aperture then, yeah, you should get shallower depth of field. But the impact of the smaller sensor is to give you deeper DOF at a given zoom level and aperture so if you equalize the aperture, I'd think you should have MORE DOF, not less...

Generally, if you're shooting in hyperfocal mode (or zone focus), you're looking for more, rather than less, DOF. If you're looking for less, then you can get it by opening up the aperture all the way, but even with this very fast lens, a compact camera is the wrong place to look for really shallow DOF...

I stand corrected. Yes, considering same aperature, the DOF is deeper on the LX7

But your comment on HF shooting got me thinking. The aperture limit before onset of defraction of the LX7 is most likely lower than the LX3/5, f4.0 perhaps? So the deeper DOF is a wash.

 

[Detail Man]

No, it should actually be deeper but the qualifier was for a given zoom level and aperture . Since the lens is faster in the LX7, you can get a wider aperture at any zoom level than you could with the LX5, so if you're using the widest possible aperture then, yeah, you should get shallower depth of field. But the impact of the smaller sensor is to give you deeper DOF at a given zoom level and aperture so if you equalize the aperture, I'd think you should have MORE DOF, not less...

Generally, if you're shooting in hyperfocal mode (or zone focus), you're looking for more, rather than less, DOF. If you're looking for less, then you can get it by opening up the aperture all the way, but even with this very fast lens, a compact camera is the wrong place to look for really shallow DOF...

I stand corrected. Yes, considering same aperature, the DOF is deeper on the LX7

But your comment on HF shooting got me thinking. The aperture limit before onset of defraction of the LX7 is most likely lower than the LX3/5, f4.0 perhaps? So the deeper DOF is a wash.

For the same framing (the same image projected onto each of the image-sensors, despite their difference in size of the active-areas), and with the same pixel-resoltion existing for both image-sensors, what you state (above) appears to me to be roughly the case when I calculate the F-Number at which the main-lobe of diffraction caused light-spreading equals a diameter equal to the width (or the height) of a 2x2 photo-site array, which is:

F[max] = ( 2 ) x ( P) / ( (2.44) x (wavelength) )

where P is pixel-size (pixel-pitch).

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.