home | index | units | counting | geometry | algebra | trigonometry & functions | calculus
analysis | sets & logic | number theory | recreational | misc | nomenclature & history | physics

Final Answers
© 2000-2016   Gérard P. Michon, Ph.D.

Cameras  &  Lenses
Technical Aspects of Basic Photography

When words become unclear, I shall focus with photographs.
 When images become inadequate, I shall be content with silence.

Ansel Adams  (1902-1984)
 border
 border  border
 border
 border
 border
 border

Related articles on this site:

Related Links (Outside this Site)

DxOMark:  Camera & lens independent image-quality measurements.
Cambridge in Colour  "A Learning Community for Photographers".
Vista View 360  by  Gene Wright.
RPS Imaging Science Group Archive.  Royal Photographic Society.
 
Why You Should Stop Shooting with Small Apertures  by  Alik Griffin.

Accessories and Gadgets :

Follow-focus shifter.

Manufacturers :

Nikon (US) | Canon (US) | Zeiss (US) | Tamron (US) | Sigma (US) |

Edward Weston:  The Photographer  (1948).
Ansel Adams, Photographer  (1958)  narrated by  Beaumont Newhall.
National Geographic:  The Last Roll of Kodachrome  (2009)   Steve McCurry.
Film Photographer Profile - Markus Andersen  (2014)   by  Rob Norton.
Canon 500mm f/4 L IS USM:  How It's Made   |   Lens Review
How camera lenses are made  Discovery Channel.

 Visible spectrum accurately rendered in RGB on grey background
border
border
 International Year of Light 2015
International
Year of Light
and
Light-Based Technologies
 International Year of Light

Technical Aspects of Photography
Optics, Photometry, Sensitometry

It's an unfortunate fact of life that different manufacturers have introduced the same features under different names.  They stick to their own company jargon in commercial literature and/or for the naming and marking of their optical equipment.  Here is an equivalence table, featuring "generic" terms on the first line:

Brand FFAPS-C StabilizerPiezo Motor
NikonFXDXVibration Reduction
VR
Silent Wave Motor
SWM
CanonEFEF-S
EF-M
Image Stabilization
IS
Ultrasonic Motor
USM
Minolta DC Supersonic Motor
SSM
Sigma DCOptical Stabilization
OS
Hypersonic Motor
HSM
Tamron Di-IIVibration Compensation
VC
Ultrasonic Silent Drive
Piezo Drive  =  PZD

More rarely used concepts include: 


(2014-11-27)   Pinhole Camera
The original  camera obscura  didn't need a lens to produce an image.

 Come back later, we're
 still working on this one...

What is a pinhole camera?   |   Pinhole camera  (Wikipedia)
How to Make and Use a Pinhole Camera  (Kodak).


(2014-12-12)   Basic characteristics of a lens
Focal length, thickness, aperture, focusing distance, reproduction ratio.

The basic characteristics of a lens are:

  • f  =  Focal length  (from backplane to focal plane, if focused at infinity).
  • d  =  Optical thickness  (distance between the principal planes).
  • A  =  Aperture  (diameter of transparent disk on backplane).

Almost all lenses used in modern photography have an adjustable aperture, so the "aperture" listed among the characteristics of a lens is really the maximal possible one  (iris  fully opened  and lens focused at infinity).  In addition to the above the following parameters are measured when a lens is focused on an object at a finite distance:

  • D  =  Focusing distance  (from object to focal plane).
  • r  =  Reproduction ratio  (size of image divided by size of object).

Nikon and other manufacturers may indicate the position of the focal plane by a grove on the bodies of their cameras.  Without accessories  (extension rings or bellows)  D  has a minimum value  D0  corresponding to the normal use on the intended camera mount.  The maximum value of  r  is a function of that.

Opticians often use following variables which are functions of the above.

  • p  =  Distance from the object to the frontplane  (outer principal plane).
  • p' =  Distance from the image to the backplane  (inner principal plane).

The above definitions imply that   p  =  D-d-p'
The imaging equations for convex lenses are:

1 / f   = 1 / p  +  1 / p'     and     r  =  p'/p

Eliminating  p' ,  we obtain the relation between  D  and  r :

p   =   f  ( 1 + 1/r )   =   (D-d)) / (1+r)
or     f  (1+r)2 / r   =   D-d

With extension rings  (and/or bellows)  of total length  X,  the maximum value of the reproduction ratio is thus the solution in  r  of the above equation with  D = X+D0  which may be rewritten:

r2  +  2 r [ 1 - (X+D0-d) / 2f ] + 1   =   0

With 3 standard extension rings  (12 mm, 20 mm, 36 mm)  X  can have 8 different values  (in mm):  0, 12, 20, 32, 36, 48, 56 and 68.

This equation has a (real) solution only when  X+D0-d  ≥  4f   I recommend expressing the (positive) solution with the following numerically robust form which is much more convenient, on modern scientific calculators, than the equivalent traditional  quadratic formula  involving square roots:

r0   =   exp ( sinh-1 [ 1 - (X+D0-d) / 2f ] )

For example, published specifications for the  AF-S DX Micro NIKKOR 40mm f/2.8G  give  f = 40 mm, D0 = 163 mm  and  r0 = 1.0.  The value of  d  is given by the equation:

d   =   D - f (1+r)2 / r   =   163 - 40 (1+1.0)2 / 1.0   =   3 mm
(The intended/correct value is 0 mm for a perfectly color-corrected lens.)

The Nikon F-mount features a distance of 46.5 mm from focal plane to flange.  That should be added to the published nominal length of this lens (64.5 mm when focused at infinity)  to obtain the distance (111 mm) from the image of infinity to the front of the lens.  Subtract this from the aforementioned 163 mm and you obtain the largest extension size  (52 mm)  usable with this lens  (corresponding to the dubious case of photograhing of a backlit object nearly touching the front of a lens focused at infinity).

To reproduce old-school 35 mm film slides on a DX sensor, you need a reproduction ratio of 1.5.  which would best be achieved with an extension ring of 6.7 mm  (with the lens on its fullest macro setting).  With the smallest commercially available extension ring  (12 mm)  a reproduction ratio of 1.5 is obtained in the middle of the lens own focusing range  (it's 1.7 at full macro).

Nikon 40mm f/2.8 AF-S Micro-Nikkor Hands-on Review  by  Kai Man Wong  (DigitalRev TV, Sept. 2011).


(2014-11-28)   Depth-of-field and  hyperfocal distance.
Nearest and farthest distances in focus at an acceptable sharpness.

When an object point on the optical axis is in sharp focus, the rays emanating from it converge to a single point on the focal plane.  If it's slightly out-of-focus, then they form a cone whose apex is not on the focal plane.  That cone intersect the focal plane in a circle called the  circle of confusion.  When the diameter of that circle is small enough  (typically defined as less than 0.030 mm in 35 mm photography)  the object is in  acceptable focus.

 Come back later, we're
 still working on this one...

When a print of prescribed sharpness is desired using different formats of negatives,  we are imposed a constant ratio between the focal length and the diameter of the circle of confusion.  As a result, the hyperfocal distance is directly proportional to the focal length or, equivalently, to the size of the negative.

Therefore, the larger the format, the tighter the depth of field.

Hyperfocal distance   |   Circle of confusion (CoC)   |   Airy disk   |   Defocus aberration


(2014-11-29)   Bokeh
The aspect of out-of-focus regions.

 Come back later, we're
 still working on this one...

Shallow focus   |   Bokeh   |   Portrait


(2015-04-26)   Defocus Control
Controlling the spherical aberration of specialized lenses.

 Come back later, we're
 still working on this one...

Videos:   Nikon 135 mm f/2 DC (Michael Foley)  |  Nikon 105 mm f/2 DC (Kai Man Wong)


(2015-05-03)   A lens can be correct for more than one color:
2 colors (achromat) or 3 (APO, apochromat) or 4 (superachromat)...

The refracting index of glass  (or any other medium)  is subject to  dispersion,  which is to say that it varies from one wavelength of light to the next.  The different properties of an optical system at different wavelength are collectively known as  color aberration  (they translate into  color fringes  observed on sharply contrasted parts on an optical image).  Mirrors are immune to it, lenses aren't.

Isaac Newton,  who invented the  reflecting  telescope, once stated that it wasn't possible to build a  refracting  optical systrm free of color aberration.

It took thirty years to proove him wrong.  Kinda.   As early as 1729  (or 1733, according to some accounts)  the amateur optician  Chester Moore Hall  figured out that different kinds of glass could be used to design an optical system which forms identical images for red light and blue light  (because the index of refraction increases with wabelength in some glasses and decreases in others.

Apochromatic Lenses and Beyond :

Solving what happens at both extremities  (red and blue)  of the visible spectrum may diminish the problem in the middle as well  (green)  but it doesn't quite solve it.  It would take more than 30 years before someone would design a lens with the same characteristics at three colors instead of just two  (such a lens is now call apochromatic).

 Come back later, we're
 still working on this one...

Wikipedia:   Achromat (1729)   |   Apochromat (APO, 1763)   |   Superachromat (1963)


(2015-02-01)   Zoom lenses   (Bergstein,  1955-1958)
variable focal length  and stable focusing distance.

A true  zoom lens  ought to be  parfocal  (i.e,  its focusing distance remains stable when the focal length changes).  The older term  varifocal  is the general  term still used for systems with variable focal length which need not meet this requirement.

The general theory of  parfocal  zoom lenses was worked out in 1958  (using Chebyshev polynomials)  by  Leonard Bergstein  (1928-2008)  who happens to be my  "scientific grandfather"  (as the second doctoral advisor of  Judea Pearl  at the  Brooklyn Polytechnic Institute,  in 1965).

In 1955, well before completing his doctoral dissertation, Bergstein applied for a patent covering some of his methods, which was granted in 1959  (US Patent 2906171).

 Come back later, we're
 still working on this one...

General Theory of Optically Compensated Varifocal Systems  (1958)  by  Leonard Bergstein (1928-2008).
Wikipedia :   Zoom lens   |   Varifocal lens


(2014-11-27)   Autofocus  (powered focusing)
Reacting to distance to mechanically adjust the focus of a lens.

Nowadays, all autofocus cameras use  passive  focus detection which works by analyzing the light received from the scene  (as opposed to the  active  sonar, most notably used with the SX-70 Polaroid camera, which computes the distance by sending an ultrasonic signal and measuring the time it takes to bounce back from the subject).  In low-light conditions, cameras may need to shine light from an auxiliary LED for the autofocus to work properly.

 Come back later, we're
 still working on this one...

Practical difference between phase-detect and contrast-based autofocus
How Autofocus Cameras Work (contrast-based passive autofocus)
Autofocus and the importance of defocusing  by  Killian Fox  (The Guardian, 2012-01-15).


(2015-06-12)   Focus Breathing:  When focal length vary with focus.
Just a minor issue in still photography.  Critical in cinematography.

 Come back later, we're
 still working on this one...


(2015-06-12)   Darkening:  Variation of aperture with focus distance.
Extreme in macro-photography  (with extension tubes and regular lenses).

 Come back later, we're
 still working on this one...


(2014-11-29)   From large formats to tiny sensors...
The  crop factor  is  43.2666 mm  divided by the diagonal of the image.

One of the best image sensors at this writing is the 6000x4000 (24.2 Mpx) sensor used in several DX Nikon cameras  (D3300, D5300, D5500, D7100, D7200).  It's made by either Sony or Toshiba  (who knows?)  and measures 23.46 mm by 15.64 mm  (pixel size is thus  3.91 microns,  or 3910 nm).

This has the same aspect ratio  (3/2)  as a 36 mm by 24 mm full-frame.  The  crop factor  is simply the scale between the two, namely  1.5345.

For dissimilar formats  (different  aspect ratios)  the  crop factor  is defined as the ratio of the respective diagonals,  since the angular coverage of a lens of given focal length always pertains to the diagonal of the image.

For example, the Panasonic Lumix DMC-ZS25  (labeled Lumix DMC-TZ35 in Europe)  has a sensor with a  4/3  aspect ratio  (6.08 mm  by  4.56 mm).  The diagonal of the image is exactly  7.6 mm,  which translates into a  crop factor  of  5.693.  The native resolution is 4896 by 3672  (1242 nm  pixel).

The big brother of the ZS25 is the Lumix DMC-ZS30  (a.k.a. DMC-TZ40)  which has Wi-Fi, built-in GPS, a finer monitor and a slightly larger sensor.  They both feature the same Leica superzoom:

LEICA   DC  VARIO-ELMAR  1:3.3-6.4  /  4.3-86   ASPH

The full-frame equivalent of this lens is advertised as  24-480 mm  for both cameras.  For the ZS25, it would be more accurate to say  24.5-490 mm.

Large-format plates, medium-format film, small-format, compact sensors :
ClassExample
(or code)
Diagonal
/mm
Aspect
Ratio
Width
/mm
Height
/mm
Area
/mm2
Crop Factor
8 x 10'' 325.2795 / 4203.2254516130.13301
5 x 7'' 218.4997 / 5177.8127225810.19802
4 x 5'' Tashihara 162.6395 / 4127101.6129030.26603
(120 film) (690) 102.7583 / 285.5574873.58 / 19
#2 Brownie 1001.441582.165746830.4327
Mamiya 7 89.64375 / 4705639200.48265
Hasselblad 79.19601 / 1565631360.54632
(645) 704 / 3564223520.61809
(135 film)Leica 43.26663 / 236248641
APS-H 34.530.216.75041.2541
(2001) Canon
EOS 1D
34.43303 / 228.6519.15471.2565
Half-frameYashica
Samurai
304 / 324184321.4422
APS-C 28.84443 / 224163361.5
DXNikon
D5500
28.19543 / 223.4615.643671.5345
Canon 7D
Mark II
26.96953 / 222.4414.963361.6043
MFT
(110 film)
Panasonic 21.64 / 317.2812.962242.0031
Four ThirdsOlympus, Kodak 19.054 / 315.2411.431742.2712
CompactLumix
ZS-25
7.64 / 36.084.56285.6930

The APS acronym in some of the above formats stands for  Advanced Photo System,  the pompous name given to a large  (technically misguided)  effort for mass-marketing a small format of film photography just before the dawn of digital photography.  That started in 1996.  New cameras were no longer produced by 2004 and the manfacture of films stopped completely in 2011.

Nevertheless, the format was a reference for a while.  Just enough time for the next generation of smaller digital sensors to be marketed as "APS-C" format, which now stands  (although  APS  itself is all but forgottten).

APS allowed the film to record additional information besides the image itself.  Some of that could be printed on the back of the photos and there were also instructions to the photofinisher to crop the image in one of the three following ways  (that could be overriden by special order, since the whole image was on film).

  • APS-H :   The whole image  ("High Definition")  30.2 16.7 mm.
  • APS-C :   Cropped central part  ("Classic")  25.1 16.7 mm
  • APC-P :   Horizontal view  ("Panoramic")  30.2 9.5 mm

Photofinishers used machines using paper rolls with a uniform width of  4''  to produce 4x7'', 4x6'' and 4x11'' prints, respectively.

Some throw-away cameras offered only a choice between "H" and "P",  as "C" was soon perceived as redundant.


(2015-06-11)   Handheld Shots Require Fast Shutter
Make the shutter speed greater than the focal length in mm.

For example, with a handheld  300 mm  telephoto lens, your shutter speed should be  1/320 s  of faster,  or else you need a tripod.

This traditional rule of thumb is only a starting point:  You may use a slower shutter speed if you have a very steady hand.  Use a faster one if you have less tolerance for blur and/or expect to produce larger prints.

This is all based on the acceptable blur induced by camera-shake for a typical size of a finished printed image.  With a smaller sensor, the same print size requires an additional enlargement by a factor equal to the  crop factor.  All told, your shutter must be faster in the same proportion.

Another way to state the same thing is to say that the above rule-of-thumb applies to the "full-frame equivalent" of the focal length.  A  300 mm lens with a  Nikon DX camera  (1.5345 crop factor)  is equivalent to a  460 mm lens  with a full-frame camera and must, therefore, be shot at  1/500 s  or faster  (the aforementioned  1/320 s  is too slow).


(2015-05-09)   ISO scale of light sensitivity
The modern scale is the direct descendant of the ASA and DIN ratings.

In practice, the sensitivity scale we now use obeys the  "Sunny 16 Rule",  which states that a film will be correctly exposed on a sunny day if the aperture of the lens is  f/16  and the shutter speed is the reciprocal of the sensitivity  (e.g., 1/100 s  for an ISO 100 sensitivity).

One degree of light sensitivity corresponds to  1/3  of an f-stop
ISO  (ASA) 2550 6480 100 125160 20040080016003200
°ISO  (DIN)  15°18° 19°20° 21° 22°23° 24°27°30°33°36°

The DIN arithmetic progression is a logarithm of the ASA geometric progression which doubles every third degree  (it's approximately multiplied by 10 every 10-th degree).  Strictly speaking, the above ISO numbers are just names for the terms of a geometric progression whose common ratio is the Delian constant,  which we may give with ludicrous precision:

2 1/3   =   1.259921049894873164767210607278...

If we assume that the round ISO values (100, 200, ...) are exact, the traditional ASA numbers 64 and 125 are not correctly  rounded from the true values  (62.996... and 125.992...)  which beg to be rounded to 63 and 126 respectively.  However, the traditional designations relate better to ASA sensitivities of 16 and 32 on one end and 250, 500, 1000... on the other.  The choice of  160  to represent 23° merely makes the aforementioned rule of thumb easy to apply  (adding 10° gives an ISO number 10 times as large, namely 1600).  This latter rule breaks down for the denominations of very high sensitivity.  Thus, 45° is quoted as  ISO 25600,  by doubling 8 times from 31° (ISO 1000) rather than multiplying by 100 from 25° (ISO 250).

Such minute details are needed only if you are writing photography-oriented programs and want to properly display traditional values while working internally in exact increments of 1/3 of an f-stop for all exposure parameters  (ISO, aperture and shutter speed).


(2015-05-15)   Photographic film sensitivity and grain size.
Chemistry of light-sensitive films and plates.

 Come back later, we're
 still working on this one...

Sensitometry   |   Photographic film   |   Film speed


(2015-05-09)   Sensor sensitivity
For a given electronic technology, sensitivity is proportional to pixel area.

 Come back later, we're
 still working on this one...


(2015-06-13)   Image noise.  Signal-to-noise ratio for shot noise.
In low-light, the number of photons received by each pixel fluctuates randomly.

 Come back later, we're
 still working on this one...

 Bayer filter

(2015-05-23)   Bayer filters
How color-vision is given to an array of photodiodes.

Each photodode is essentially a monochrome device.  In scientific applications  (aboard the  Hubble Space Telescope, for example)  arrays of identical photodiodes are only used to capture monochrome images unrelated to human color vision.  Uniform filters can be placed in front of the entire sensor to let it capture the image for a specific part of the optical spectrum  (call it a color if you must, but this can also be a slice of near infra-red (IR) or ultra-violet (UV).  If needed, three exposures with different filters can be rendered in "false colors" by assigning arbitrarily a specific visible color to each shot.  True colors are just a special case of this, engineered to reproduce the  photopic  (bright-light)  color-response of the human eye.

In ordinary color photography, we can't proceed this way.  For one thing, we'd rarely have the luxury of taking three different shots of exactly the same object.  We must use a single brief exposure to gather as much information as possible about both the intensity and the color of the light received by every pixel of the array.

For this, a special mosaic of small filters is used to make neighboring cells react differently to light of different colors  (just like the human retina has four kinds of light receptors with different sensitivities and spectral responses).

Solid-state digital color cameras use almost exlusively the  Bayer filter  consisting of a regular pattern where each square of four adjacent pixels include one red, one blue and two greens.  This mimic roughly the human eye, which is more sensitive to the middle of the visible spectrum  (green)  than to either extremity  (red and blue).  The was originally designed, in 1974, by  Dr. Bryce E. Bayer (1929-2012)  who spent his entire career  (1951-1986)  at  Eastman Kodak.

The basic resolution of a sensor is the size of its elementary pixel  (although the exact brightness and color assigned to that pixel depend on what the photodiodes corresponding to neighboring pixels detect).

 Come back later, we're
 still working on this one...

Color filter array   |   Bayer filter


(2015-06-13)   Effective and actual digital sensor sizes:
Information is also collected just outside the nominal active sensor area.

 Come back later, we're
 still working on this one...


(2015-05-09)   Exposure time, "shutter speed"

 Come back later, we're
 still working on this one...


(2015-05-02)   Exposure Value (EV) and Exposure Index (EI)
Metering light.  Reciprocity corrections for long exposures.

Before the digital era, a camera was normally loaded with film of a given ISO sensitivity well before decisions were made concerning other means of controlling the exposure.  For a given film, the proper exposure was thus measured as an  exposure index  (EI) defined as the product of the shutter speed into the square of the f-stop number.

Actually, film doesn't quite react to light in proportion of the time elapsed...  In pratice, this means that a correction should be applied for very long exposures.  That correction depends on temperature.  This, however, is a chemical property of sensitive film, not of light itself.

The amount of light received by a unit area of the sensor is just proportional to the product of the exposure time into the square of the relative aperture  (assuming a circular iris)  divided by the optical density of the system:

t A2 / d

A factor of 2 in exposure is traditionally called  one f-stop.  The term comes from the old-school construction of aperture rings with clicks regularly spaced at intervals corresponding to a factor of root 2:

1.4,   2,   2.8,   4,   5.6,   8,   11,   16,   22,   32,   44,   64,   90,  128,  181 ...

From on such "stop" to the next, the illumination doubles.  Lenses with apertures faster than  f/1.4  have been produced, but they are quite rare.

Because it was natural to set an  aperture ring  "a little bit" above or below a full stop, the practice arose to divide f-stops into  thirds  as tabulated below.

Normalized aperture denominations   (rounded values of  2n/6 ,  for  n = 0 to 41)
1.01.42 2.845.6 811162232 446490
1.11.62.23.24.5 6.3912182536 5172102
1.31.82.5 3.557.110 142028405780114

Manufacturers usually align the ratings of theirs lenses on the highlighted entries of the above table.  However, a few lenses have been made with apertures corresponding to half-stops  (e.g., 1:1.2 or 1:1.7).  and modern digital cameras can accommodate photographers who prefer half-stops:

Half-stop aperture denominations   (rounded values of  2n/4 ,  for  n = 0 to 27)
1.01.42 2.845.6 811162232 446490
1.21.72.43.3 4.86.79.513192738 5476108

In borderline cases, all of the above standard denominations were rounded  down  from true values,  probably for marketing reasons  (for example, 3.5 stands for 3.5636).  The only exception is  1.3,  at one third of a stop below 1.4  (it's rounded  up  from  1.26  to avoid a clash with the standard half-stop standard denomination of  1.2).

Likewise (grey entries aboe) 12.6992 should be rounded down in the third-stop scale to avoid a clash with the half-stop denomination of 13  (rounded down from 13.4543...).  Unfortunaly, this fact was lost on Nikon and others.  In a modern camera which allow photographers to switch between the third-stops and half-stop aperture scale, this mistake allow ambiguous report of "13" apertures in the metadata associated with pictures  (the good news is that the two relevant apertures have different unternal representations ($58 and $5A respectively)  and they would simply read correctly as 12 and 13 once the reading software is fixed, even for pictures taken many years ago.  Resurrecting the 12.5 rating of the old German aperture scale could be appealing but the longer string would increase clutter on our tiny LCD screens...
 
The preferrence toward rounding down extends to high apertures  (e.g., 1:28 or 1:80)  for consistency with the familiar denominations used at wide aperture.  Old-school photographers know that a factor of 10 in aperture is meant to denote  62/3  f-stops:

210/3   =   10.0793683991589853181376848582...

The multiples of 1/6 of an f-stop would include all of the above.  The  internal operations  of modern digital cameras by Nikon  (and, presumably, other manufacturers)  rely on a unit exactly twice as fine  (1/12 of an f-stop)  which corresponds to an increase of  2.93%  in the diameter of the lens iris:

2 1/24   =   1.0293022366434920287823718...

In theory, that unit could accomodate a user interface in terms of quarters of a stop as well.  However, I have never seen such a thing in actual use or even heard of it, except on the  Wikipedia page on that topic  (I consider the relevant section utterly misguided).  If it was used at all, a quarter-stop aperture scale couldn't  possibly  use 2-digit abbreviations without conflicting with the above well-established ones.

In photography, narrow apertures  (beyond 1/32 or so)  are rarely used,  if ever,  because  diffraction  would then ruin the optical quality of a lens.  For all practical purposes, the above tables already represent an  overkill.

Aperture Scales on the Rings of Old and New lenses :

The aperture ring of a modern lens bears the following numbers:

  • The maximal aperture, at one end of the scale.
  • Part of the above full-stop sequence: 1.0, 1.4, 2, 2.8, 4, 5.6, 8...

Before  WWII, an old German aperture scale could be used instead.  It was defined backward from a tiny aperture exactly equal to  f/100.

The  First Type  of German aperture scale disappeared after  WWII
1.11.62.23.24.56.39 12.51825365071100

The first of those abbreviations can be found in the second line of our first table, which means that they represent apertures located very nearly 1/3 of a step above a modern full stop.  In practice, that's good enough to use such lenses successfully with modern external light-meters.

To compute the precise difference between the two scales, let's divide by 100 the exact value of the counterpart of  f/100  in our modern scale:

2 20/3 / 100   =   1.0159366732596476638410916...

Thus, apertures in the old German scale are about 1.6% larger than their matching modern counterparts.  (they let in about 3.2% more light).  The diference is utterly negligible.  It corresponds to 1/22 of an f-stop, which is about  half  of the smallest aperture unit  (1/12 of an f-stop)  used by digital cameras for internal computations.

 Leitz Summitar, f = 5cm 1:2, Serial No. 607225. 
 Old German aperture scale.   Leitz Summitar
f = 5cm 1:2
M39 Leica mount

 
Made in 1946, this is a rare example of a post-war lens using the old German aperture scale.
 
Photo courtesy of Nettax,  Sweden

As opposed to the current full-stop aperture scale, which was called  unternational,  the obsolete one was variously called  EuropeanGerman  or  continental.

Reciprocity failure


(2015-05-02)   Neutral Density Filters
A powerful option to control exposure in critical cases.

  • Transmittance  (< 1)  is the ratio of light transmitted to light received.
  • Opacity  (> 1)  is the reciprocal of transmittance.
  • Optical density (> 0)  is the decimal logarithm of opacity.

Density   =   log10 ( 1 / Transmittance )   =   log10 ( Opacity )

Thus, a transmittance of 25%  ( ¼ )  corresponds to the following density:

log ( 1 / 0.25 )   =   log (4)   =   0.60206

Using the usual approximation of  0.3  for the common logarithm of 2, this is always quoted as a density of 0.6.  Several identifications are used for such a filter by different manufacturers, namely:

  • "ND 0.6"   because the optical density is  0.6  (Kodak, Tiffen, Lee).
  • "102" or "2 BL" (B+W)   since light is blocked by  2  f-stops.
  • "ND4", "NDx4" (Hoya) or 4x (Leica).  Factor of  4  in shutter speed.

B+W  (owned by Schneider-Kreuznach since 1985)  now goes to the trouble of printing up to 4 markings  (of all 3 above types).  For example, the ring of their  (52 mm millimeter diameter)  filter with 0.1% transmission reads:

        B+W   52   110   ND 3.0   -   10 BL   1000x   E

Most manufacturers aren't this redundant.  Normally, the clear differences in the above formats are sufficient to avoid ambiguities.  However, the very common NDx2 and NDx4  filters  (one and two stops, respectively)  are often advertised as ND2 and ND4, which has confused some mail-order buyers looking for rare  ND 2.0  or  ND 4.0  dark filters  (NDx100 and NDx10000 respectively;  6.6 and 13.3 f-stops).

Typical markings on neutral-density filters for a given transmittance  (%)
50%25%12.5%6.25%3.125%1.56%1%0.78%
ND 0.3ND 0.6ND 0.9ND 1.2ND 1.5ND 1.8ND 2.0ND 2.1
101102103104105106 107
x2x4x8x16x32x64x100x128
ND2ND4ND8ND16 

The list goes on with very opaque filters like  ND 2.6 = x400  (0.25% transmittance = 8.6 stops).  The popular 10-stop filter  (0.1% transmittance)  can be marked  ND 3.0,  110,  10 BL  or  x1000  (instead of x1024).  Such opaque filters allow tripod shots at low shutter speeds in bright conditions,  so that waterfalls or foliage are just a blur in broad daylight...

The cost of extremely opaque filters is often prohibitive, in part because the market for them is so small.  You can still find "113" filters sold as  ND 4.0  (X10000, actually 13.3 f-stops)  in the form of glass or gel filters from Lee or Kodak (Wratten)  but they're almost extinct.  Expect to pay around  $100  for just a square of optical gelatin...

It All Starts with Thread Size and Rings!  by  Ching-Kuang Shene,   Michigan Technological University.


(2015-05-30)   Cut Filters
Selecting only part of the  IR, visible and UV spectra.

The best known and cheapest ones are the mass-produced "UV filters" (L37) which photographers often purchase as sacrificial glass to provide mechanical protection for the front elements of their expensive lenses.

 Come back later, we're
 still working on this one...

Hoya optical glass is transparent until  2700 nm  or so, at which point the transmittance falls sharply to reach  50%  at  2750 nm.  Then, there's a hills-and-valleys decrease until perfect opacity is reached around  4500 nm.

Newcomer  Zomei  of Hong-Kong  (Xuzhou Bingo Network Technology Co., Ltd., mainland China)  uses RoHS-compliant HD glass from  Schott.

Equivalences Between Some Common Longpass Infrared Filters
Infrared
Jargon
50%
Cutoff
Hoya Wratten
(Tiffen)
B+WSchottZomei
(Bingo)
1050 nmRM10087a 094RG1000
930 nm87b IR 950
900 nmRM90
Black 850 nmIR-8587c 093 IR 850
760 nmIR-76 IR 760
Standard 720 nmR7288a IR 720
695 nm89b 092
Brown 665 nmR6670 RG665 IR 680
Deep Red 610 nm25A29 091
Goldie 590 nm25 090 OG 590

Proper infra-red photography produces an actual image of what the unaided human eye can't possibly see.  That point is lost on those who use touch-up software to produce fake infrared look-alikes from  very  ordinary pictures.

A color sensor behind an infrared filter may behave in unpredictable ways by capturing some residual color information.  Some amateur have managed to use that as the sole basis for beautiful false-color renditions...

That endeavor creates a dubious temptation to use sub-standard IR filters  (665 nm or 590 mm)  instead of a proper  720 mm  cut-filter.  As more visible light is allowed in,  the hope is that more color information will remain which might be usable...  That's a bad idea, because this practice is very likely to overwhelm the red channel and silence the other two.  The picture below was taken in overcast wheather at noon  (June 2015, Los Angeles)  through a 720 nm filter  (100% "de-fading" in post-processing).

 Entrance of my castle, in infrared
 (720 nm) noontime in June, 2015-06-12 11:34

If you want real false-color infrared images, bite the bullet and make three separate exposures of the same subject through at least three different proper  infrared  filters  (720 nm or longer).  With the monochrome pictures so obtained, you may separate the infrared spectrum into several channels by subtracting from every exposure the one taken with the next filter  (for the last channel, corresponding to your longest wavelength, there's nothing to subtract).  Assign to each channel a visible color of your choice before combining everything into a single picture.

Infrared Photography with a Digital Camera  by  J. Andrzej Wrotniak.
 
Hoya UV & IR Cut Filter   |   Wikipedia :   Optical filter   |   Dichroic filter


 Fraunhofer (2015-05-21)   Color temperature, tint and white balance.
Direct sunlight is  5200 K  (not 5800 K).  Shadows are 8000 K.

The average temperature at the surface of the Sun is  5778 K.  In the main, our star radiates like a blackbody at that temperature,  but there are thousands of dark  Fraunhofer lines  in the solar spectrum.  The most prominent of these were first observed by Joseph von Fraunhofer (1787-1826)  in 1814.  (That great discovery is utterly irrelevant to photography.)

The atmosphere brings another level of complexity to sunlight, because  Rayleigh scattering  is more pronounced for short-wavelength light.  Blue light is thus removed from direct sun rays and becomes visible in other directions.  Yes, that's what makes the sky blue and the Sun yellow  (or even red at sunrise/sunset, when the rays have to travel through a greater distance through the atmosheric shell).  This effectively lowers the color temperature of direct sunlight down to about  5200 K  for the better part of the day.  Conversely, shady areas on cloudless days are predominantly lit by the blue sky, which corresponds to a much higher color temperture  (8000 K).

White clouds are lit from a combination of direct sunlight and skylight which essentially yields back the same color temperature as sunlight outside the atmosphere  (5800 K  or so).  When the Sun is behind clouds but some patches of blue sky are showing, the resulting daylight has a typical color temperature of  6000 K.

Incandescent light is produced by a solid filament of tungsten, which melts at 3422 C  (that's 3695 K).  That's the highest melting point of all metals.  So, no incandescent light can possibly deliver more than  3695 K  (that's actually the color temperature of the bright flash emitted by a dying incandescent bulb, since its imminent failure is due to the melting of the filament).  Ordinary bulbs are  3000 K  or so,  some incandescent floodlights are designed to be  3400 K.  An average value of  3200 K  is often used by old-school photographers.

Fluorescent light is entirely different. 

 Come back later, we're
 still working on this one...

ExpoDisk 2.0 (2013-11-18) white-balance filter, presented in 2012 by Zach and Jody Gray  [ 12345 ]   |   Wikipedia :   Flash synchronization


(2015-06-09)   Color-conversion filters
Converting one type of color balance to another.

This type of filters has been made all but obsolete by the "white balance" setting of modern digital cameras.  On the other hand, if you're shooting color film, you need the filters to match the loaded film with a different type of light source.  Especially so with color slides, which lack the flexibility of applying color correction at printing time.

The traditional Wratten numbers are just reference numbers which are not based on any particular piece of information.  (The system was conceived well before fluorescent lighting existed and Kodak/Tiffen extended it with two trademarked mnemonics later.)

By contrast, the Hoya numbers correspond to differences between the "milred" ratings of the color temperatures involved  ("micro reciprocal degrees").  The sign of that difference is specified either by an "A" for  amber  or a "B" for  blue.  Thus, the numerical rating for their conversion between the two common types of tungsten light is:

1000000 ( 1/3200 - 1/3400 )   =   18.38235...   rounded to   20

Conversions between daylight and tunsgten use  3300 K  for the latter:

1000000 ( 1/3300 - 1/5500 )   =   121.2121...   rounded to   120

Some Common Color-Correcting Filters  (balancing filters)
AspectDensity Wratten LightFilm Hoya
blue 80a3200 K5500 KLB-120
pale amber 81a3400 K3200 KLA-20
pale blue 82a3200 K3400 KLB-20
amber 85b5500 K3200 KLA-120
purple FL-D Fluorescent5500 K FL-DAY
FL-W
purple FL-BFluorescent3200 K

The first five filters listed above were commonly carried by most serious photographers in the film era.  They can be stacked.  For example,  an FL-B filter is equivalent to an FL-D stacked with an  85b  (except that the latter combination is darker).


(2015-05-10)   Flash photography
The  guide number  (GN) is defined in distance units, assuming ISO 100.

When a light source emits a pulse of luminous energy in the direction of a object at distance  d,  each unit of surface of the object  (measured perpendicularly to the direction of a light ray)  receives an amount of light  (luminous energy)  inversely proportional to the square of the distance  d.

On the other hand, the sensor of a camera observing an object at distance  d'  receives from it an amount of light proportional to the square of its relative aperture.

If the light source is a flash unit mounted on the camera, the distances  d  and  d'  are approximately equal.  As  d  varies,  for the sensor to receive the same amount of light  (inversely proportional to its sensitivity measured in ISO units)  the product of the aperture into the distance must be a constant, called  guide number

Since the relative aperture is a dimensionless number, the  guide number  has the dimension of a distance and is expressed in the same units as  d.  The more powerful the flash, the greater the  guide number.

The above relationships of proportionality can be expressed by the following formula involving a universal constant  S  with the dimension of a surface area, and actually proportional to the luminous energy of a flash pulse.

S / (ISO)   =   (guide number)2   =   (distance x aperture)

For example, Nikon's SB-500 has a GN  (at 100 ISO)  of 24 m  (or  78.74 ft, rounded to  79 ft).  In metric countries, the unit of distance is often omitted  (as it's understood that photographers ought to measure distances in meters).  Knowing that the guide number is proportional to the square root of the ISO,  we may tabulate it for various sensitivities:

Guide numbers  (GN)  of Nikon's SB-500 Speedlight for different ISO sensitivities :
ISO 6480 100125160 200250320 400500640 80010001250 1600
GN 1921 242730 343843 485460 687686 96

To double the  GN  for a given flash,  we must multiply the  ISO  by 4.  Nikon says that the built-in flash of the  D5500  DSLR  has a standard guide number  (at ISO 100)  of  12 m.  So,  the  SB-500  is  4  times more powerful.

The  beam width  of a flash unit is often given in term of the focal length  f  of the widest lens whose field of view it would cover  for a full-frame sensor  (24 mm  by  36 mm).  Using the theorem of Pythagoras,  the diagonal of a full-frame is  do = 43.2666153...mm  (or nearly 649/15).  Therefore,  the  angular diameter  q  of the beam is given by:

½ do / f   =   t   =   tan ( q/2)       or       q   =   2 atan ( ½ do / f )

Thus,  in the case of the aforementioned  Nikon SB-500 AF Speedlight,  the manufacturer specification  f = 24 mm,  translates into:

q   =   2 atan ( 21.6333 / f )   =   1.467   =   84°

Focused Flash Beams :

Flash units with  zoom heads  have several settings which can be selected either manually or automatically to match the angular field-of-view of the lens used by the camera.  The automatic selection, involving a motorized optical system, is very useful when the flash is mounted on a camera with a zoom lens.

Now, the solid angle subtented by a conical beam of angular diameter  q  is:

W   =   4p sin2 (q/4)

For a given source, if we let the angle  q  vary the luminous energy received by an object within the focused beam is inversely proportional to the above solid angle  W  of the bean. 

 Come back later, we're
 still working on this one...

This can be used to derive the  guide number  at any zoom-head setting from the manufacturer's rating at the narrowest one  (in bold below).

Examples of Guide Numbers  (GN)  at  ISO 100, in meters or feet.
Beamwidth
Setting
f 24 mm28 mm35 mm50 mm70 mm85 mm105 mm
q 96°75.4°63.4°46.8° 34.3°28.6°23.3°
$125Yongnuo
YN568EX
28 m
92 ft
30 m
98 ft
39 m
128 ft
42 m
138 ft
50 m
164 ft
53 m
174 ft
58 m
190 ft
$380Canon
580EX II
28 m
92 ft
30 m
98 ft
n/a 42 m
138 ft
50 m
164 ft
53 m
174 ft
58 m
190 ft
$200Nikon
SB-500
24 m
79 ft
No zoom head.
Nikon D5500
built-in flash
12 m
39 ft
No zoom head.

Table based on manufacturer specifications.  Canon's 580EX II not tested.

Diffusers :

There are two types of diffusers, which serve different purposes:

  • Transparent diffusers  just increase the angle of the beam (for use with a wide-angle lens, if the flash unit is mounted on the camera). 
  • Diffusion screens and light boxes  will, in addition to the above, increase the size of the light source  (which transparent diffusers don't change much)  which will soften the shadows created by the flashlight.

For example, when the buit-in transparent diffuser of the YN568EX is used, the zoom goes automatically to its widest  (24 mm)  position and the unit's LCD displays a focal length of  14 mm, corresponding to a beam diameter of  114°, as estimated by the manufacturer.  The GN is then about  15 m.

Honeycomb Grids :

This is roughly the opposite of a diffuser.  A grid narrows the beam of light in a specific way; the finer (and thicker) the grid, the narrower the beam.

This works mostly by eliminating slanted rays, which have to undergo many imperfect reflections to go through the grid.

Flash Synchronization :

The first camera with a built-in flash socket, activated by the shutter, was introduced by Exakta, in 1935.

One mainstay of flash photography are small coaxial cables with 3.5 mm (1/8") male connectors at both ends, matching  PC sockets.  The abbreviation stands for Prontor/Compur  and is named after two brands of camera shutters, made by two distinct manufacturers of which  Zeiss  was a major shareholder  (Compur from 1951, and Prontor from 1953 forward).  The dimensions were standardized,  as ISO 519,  in  1974  and  1992.  Electrically, the connection is simply an open circuit when inactive and a short circuit when active.

Several synchronization signals were generated by mechanical cameras for different flash technologies.  All of them were implemented in the legendary  Nikon F.  Only  "X"  synchronization survives today,  to drive electronic flash units.  The first three modes listed below  (now obsolete)  were designed for magnesium-burning bulbs, which reached their peaks a few milliseconds after ignition.

  • M  (Medium).  Active  20 ms  before the shutter is fully open.
  • F  (Fast).  Active  5 ms  before the shutter is fully open.
  • FP  (Flat Peak).  Long-burning bulbs designed for focal-plane shutters.
  • X  (Xenon).  Active as soon as the shutter is fully open.

Actually, the pulses of light emitted by modern Xenon tube are so short that they can\ be emitted at any time the shatter is open.  Doing it just before the shutter closes is known as  rear-curtain  synchronization.  That approach allows the dim motion trail of a moving object to be captured during a long exposure, ending with a sharp flashlit image frozen in time.

AFP:  Stroboscopic flashing for fast focal-plane shutters.

FP syncrhonization is often transluterated as  focal plane.  The specialized  FP bulbs  provided a constant illumination between the time when the front curtain started and time when the rear curtain arrived.  This way, every part of the film received the same amount of light,  even at high shutter speeds  (achieved by allowing only a small slit between the two moving curtains).

Nowadays, the equivalent of an  FP  bulb can achieved by strobing an electronic flash very rapidly throughout the time the curtains travel.  This is called  AFP  (Auto FP)  by Nikon and HSS  (High-Speed Sync.)  by Canon.

AFP  (HSS)  solves a problem with no other solutions:  A poorly-lit fast-moving subject in front of a bright background.  A fast shutter is needed to freeze the motion  (say  t = 1/4000 s)  but a flash in the usual X-mode can't be used to light up the subject because it the camera would then require a relatively slow shutter speed  (say  T = 1/200 s)  which would overexpose the background.

Another case is often quoted where a blurry background is desired  (hence wide aperture and fast shutter)  with a static subject.  However, this can be captured without AFP  (using neutral density filters).

AFP  (HSS)  effectively uses only a fraction of the energy delivered by the flash unit.  That fration is equal to the nominal exposure time  (t)  divided by the time  (T+t)  during which stroboscopic illumation must be maintained because part of the image sensor is exposed.

To compute the latter duration, we assume the flashes have negligible duration.  The time it takes for one curtain to travel the focal plane is then seen to be equal to the shortest shutter time which ensure that the entire sensor is exposed at some instance.  This is a critical characteristic of the camera which is well advertised as the fastest shutter speed at which an electronic flash is usable with  X-synchronization  (T = 1/200 s,  in our example).  Now, "flat" illumination must be maintained between the departure of the front curtain until the arrival of the rear curtain, which is roughly the aforementioned duration  T+t.

Each point of the sensor receives only a fraction  t / (t+T)  of the total stroboscopic light emitted:

1 / (T/t + 1)   =   1 / (4000/20 + 1)   =   1 / 21

As every photographer who ever used this technique knows, it's thus very wasteful in terms of luminous energy.  In our numerical example, the drain on the units's battery is at least 21 times what would have been required to properly expose the subject with a single strobe at low shutter speed.

If the frequency of the flash unit is an exact multiple of  1/t,  then the illumination will be perfectly uniform  (regardless of the shape of each pulse, assuming they are all alike).  Now, notice that all standard exposure times above  1/8000 s  in steps of half an f-stop are exact multiples of  1/24000.  So, if the unit delivers its pulses at a frequency of  24000 Hz,  that condition is met for any camera that aligns its shutter speeds precisely at half-stops, using the nominal values:

Whole stops and half-stops exposure times as exact multiples of  1 ms / 24
3468 12162432 486496
1/80001/60001/40001/3000 1/20001/15001/10001/750 1/5001/3751/250

There's no need to go beyond that table, as the technique is utterly useless when ordinary flash photography applies  (usually, at 1/200 s or slower).

On the other hand, if the unit's stroboscopic frequency is unrelated to the exposure time, it must be large enough to ensure that every point is exposed to an average number of flashes sufficient to make the contribution of one extra pulse fairly irrelevant, in relative terms...

For example, if flash pulses at some frequency around  100 kHz  are used with a  1/8000 s  exposure time,  each pixel sees between 12 and 13 pulses.  The maximum deviation from the  geometric mean  of  12.49  is 4%,  which corresponds to the following peak-to-peak amplitude, measured in f-stops:

log 2 ( 13 / 12 )   =   0.115477...       (about  1/9  of an f-stop)

The resulting light-and-dark bands are barely detectable.  Still, for  AFP/HSS  photography, it's a good idea to use stroboscopic light at  24 kHz  (or a multiple thereof)  to take advantage of the above numerical remark...  If  96 kHz  is chosen, there's no banding in 75% of the choices of standard shutter speeds  (including 1/8000 s and   1/6400 s).  The worst banding is for  1/5000 s,  if you absolutely insist on that shutter speed:

log 2 ( 20 / 19 )   =   0.074       (about  7.4%  of an f-stop)

If the clock of the camera and the clock of the flash unit are slightly off,  low-contrast bands are indeed produced, but they are much too wide to be noticed  (wider than the picture itself, for crystal-controlled clocks).

Focal-plan shutters.
Rear-curtain sync.
Auto focal-plane (AFP) = HSS sync.

 Come back later, we're
 still working on this one...

Nikon Auto-FP Flash Mode   |   Wikipedia :   Flash synchronization

border
border
visits since June 2, 2015
 (c) Copyright 2000-2016, Gerard P. Michon, Ph.D.