the last word

Photography meets digital computer technology. Photography wins -- most of the time.

  • site home
  • blog home
  • galleries
  • contact
  • underwater
  • the bleeding edge
You are here: Home / The Last Word / What’s your Q?

What’s your Q?

May 6, 2014 JimK 4 Comments

Another way of looking at the minimum resolvable distance between two points is to turn it on its head and look at spatial frequencies. When we do that, we can restate one of the conclusions of this post as: the upper cutoff spatial frequency of a diffraction–limited lens is one over the Sparrow distance, or

Fclens = 1 / lambda * N, where lambda is the wavelength of the light, and N is the f-stop.

Now let’s turn our attention to the upper spatial frequency a sensor can resolve. A consequence of the Nyquist criterion is that the spatial frequency cutoff of a sensor is

Fcsensor = 1 / (2 * pitch) where pitch is the sensel pitch.

In the ground imaging world (satellites, aerial photography) a digital optical capture device is “balanced” when the two frequencies are equal. There’s another, less binary way of looking at the question of lens and sensor balance; the Q of an imaging system is defined as:

Q = 2 * Fcsensor / Fclens

So

Q = 2 * (lambda * N) / (2 * pitch) = lamda * N / pitch

I’ve included some references at the end of this post. For systems that image a range of frequencies, like normal photographic digital cameras, the convention is to set lambda equal to the average of the highest and lowest imaged wavelength, or, for systems imaging visible light,

lambda = (380 + 720) / 2 = 550 nanometers.

Since we will be working in micrometers, let’s call it half a micrometer.

At a Q of 2, the system is balanced; the diffraction of the lens is just enough to provide the proper AA filter to the sensor. For Q’s of greater than that, the sensor can resolve more detail than the lens can supply, and for Q’s of less than that, the lens can supply more detail than the sensor can resolve, and aliasing can result.

High-resolution full frame cameras like the Nikon D800e and the Sony alpha 7R have pixel pitches of slightly finer than 5 micrometers.

The Q of a diffraction-limited f/11 system with a sensor pitch of 5 micrometers is:

Q = (0.5 * 11) / * 5 = 5.5/5 = 1.1

The sensor can’t resolve all of the lens’s detail.

How fine a pitch would we need to have a balanced system with a diffraction-limited f/11 lens?

pitch = lambda * N /Q = 0.5 * 11 / 2 = 2.75 micrometers.

As you can see, using Q = 2 as a definition of balance between the lens and the sensor yields desirable pixel pitches that are much finer than what are commonly thought to be adequate.

Next, a discussion of the consequences of removing some of the assumptions.

Reference:

http://kiss.caltech.edu/workshops/gazing/presentations/green.pdf

The Last Word

← Who are you going to believe, me or your own eyes? Interpreting Q in the real world →

Trackbacks

  1. Interpreting Q in the real world | The Last Word says:
    February 11, 2016 at 12:06 pm

    […] off, let me dissuade you from one possible – and erroneous – interpretation of the findings of the last post: “Well, gee, if the sensor can’t resolve all of the detail that my lens can put out at f/8, why […]

    Reply
  2. Bridging the CoC/MTF50 gap | The Last Word says:
    June 5, 2016 at 7:06 am

    […] earth imaging systems for example, the have a concept of image Q which balances the two. You can read about it here. In those systems, it is common to sample more finely with respect to lens resolution than we do in […]

    Reply
  3. Diffraction and ultimate FF pixel count says:
    July 31, 2019 at 12:34 pm

    […] https://blog.kasson.com/the-last-word/whats-your-q/ […]

    Reply
  4. Interpreting Q in the real world says:
    February 2, 2020 at 1:28 pm

    […] off, let me dissuade you from one possible – and erroneous – interpretation of the findings of the last post: “Well, gee, if the sensor can’t resolve all of the detail that my lens can put out at f/8, why […]

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

March 2023
S M T W T F S
 1234
567891011
12131415161718
19202122232425
262728293031  
« Jan    

Articles

  • About
    • Patents and papers about color
    • Who am I?
  • Good 35-70 MF lens
  • How to…
    • Backing up photographic images
    • How to change email providers
  • Lens screening testing
    • Equipment and Software
    • Examples
      • Bad and OK 200-600 at 600
      • Excellent 180-400 zoom
      • Fair 14-30mm zoom
      • Good 100-200 mm MF zoom
      • Good 100-400 zoom
      • Good 100mm lens on P1 P45+
      • Good 120mm MF lens
      • Good 18mm FF lens
      • Good 24-105 mm FF lens
      • Good 24-70 FF zoom
      • Good 35 mm FF lens
      • Good 60 mm lens on IQ3-100
      • Good 63 mm MF lens
      • Good 65 mm FF lens
      • Good 85 mm FF lens
      • Good and bad 25mm FF lenses
      • Good zoom at 24 mm
      • Marginal 18mm lens
      • Marginal 35mm FF lens
      • Mildly problematic 55 mm FF lens
      • OK 16-35mm zoom
      • OK 60mm lens on P1 P45+
      • OK Sony 600mm f/4
      • Pretty good 16-35 FF zoom
      • Pretty good 90mm FF lens
      • Problematic 400 mm FF lens
      • Tilted 20 mm f/1.8 FF lens
      • Tilted 30 mm MF lens
      • Tilted 50 mm FF lens
      • Two 15mm FF lenses
    • Found a problem – now what?
    • Goals for this test
    • Minimum target distances
      • MFT
      • APS-C
      • Full frame
      • Small medium format
    • Printable Siemens Star targets
    • Target size on sensor
      • MFT
      • APS-C
      • Full frame
      • Small medium format
    • Test instructions — postproduction
    • Test instructions — reading the images
    • Test instructions – capture
    • Theory of the test
    • What’s wrong with conventional lens screening?
  • Previsualization heresy
  • Privacy Policy
  • Recommended photographic web sites
  • Using in-camera histograms for ETTR
    • Acknowledgments
    • Why ETTR?
    • Normal in-camera histograms
    • Image processing for in-camera histograms
    • Making the in-camera histogram closely represent the raw histogram
    • Shortcuts to UniWB
    • Preparing for monitor-based UniWB
    • A one-step UniWB procedure
    • The math behind the one-step method
    • Iteration using Newton’s Method

Category List

Recent Comments

  • JimK on Sony 135 STF on GFX-50R, sharpness
  • K on Sony 135 STF on GFX-50R, sharpness
  • Mal Paso on Christmas tree light bokeh with the XCD 38V on the X2D
  • Sebastian on More on tilted adapters
  • JimK on On microlens size in the GFX 100 and GFX 50R/S
  • Kyle Krug on On microlens size in the GFX 100 and GFX 50R/S
  • JimK on Hasselblad X2D electronic shutter scan time
  • Jake on Hasselblad X2D electronic shutter scan time
  • Piotr Chylarecki on Who am I?
  • JimK on Who am I?

Archives

Copyright © 2023 · Daily Dish Pro On Genesis Framework · WordPress · Log in

Unless otherwise noted, all images copyright Jim Kasson.