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Number 30

Disclaimer: All the below text are my personal thoughts, so they don't have to reflect the thoughts of the people that made the formula/guidelines.

I have the stereophographic guidelines also as functions (Add-in) for Excel available, so one can build one's own application around this Excel Add-in. If you want more information, let me know (remove underscore in presented e-mail address)!

Stereo glossary: some definitions

 Purple definition is not used on my web site, but given because other people sometimes use these definitions.
a'c
lens to film/chip distance [mm] (1/a'c=1/Fc-1/focusdistance)
nearestobjectact distance nearest object in actual scene [mm]
nearestobjectexp distance nearest object in experienced image [mm]
farthestobjectact distance farthest object in actual scene [mm]
farthestobjectexp distance farthest object in expereinced image [mm]
b0
stereo base [mm]
CoC
Angular Circle of Confusion [°], sometimes also in [mm]
deviation
The 2D displacement [mm or pixel] of homologous points in the stereo pair, which is a result of a certain depth in the 3D scene. This term is equivalent with OxD.
The deviation is the difference between the 'homologous separation of the point under investigation' and the 'homologous separation of the farthest points'. (Ferwerda [1990], page 237)
Deviation can be in the horizontal of vertical direction (or a combination of the two, like a vector in a (2D) plane).
(some people call this parallax [mm or pixel], which seems to be true in astronomy for instance and in technical paper it is also called disparity).
DH
Hyperfocal distance, this is closest distance that is perceived as sharp when the camera lens is configured for infinity [mm]. (Hawkins [1980], page 71)
eye separation
The distance between the two optical axis of the eyes [mm]
filmwidth
width of uncropped film/chip [mm or pixel]
Fc camera's focal length [mm]
FoV
Field of View [°] is the angular part visible in the actual (act) scene or experienced (exp) image.
Fv
stereo viewer's focal length [mm]
focusdistance The focused distance [m]
HAOxD Highest Allowable On x Deviation [mm or pixel] (threshold deviation related to highest comfortable experienced parallax angle [~4°]).
x can be film/chip (F), screen/display/picture (P), viewfinder (V), retina (R), etc
image
the image is the virtual 3D scene that is seen when looking at a stereo pair, this is experienced with the brain.
LAOxD
Lowest Allowable On x Deviation [mm or pixel] (threshold deviation related to parallax angle which still gives enough experienced stereoscopic depth [~1°])
x can be film/chip (F), screen/display/picture (P), viewfinder (V), retina (R), etc
M
Magnification (a'c/focusdistance) [m]
MAOxD
Maximum Allowable On x Deviation [mm or pixel] (I think this is the same as my OOxD...)
x can be film/chip (F), screen/display/picture (P), viewfinder (V), retina (R), etc
MOxD Actual Maximum On x Deviation [mm or pixel] (due to nearestobjectact and farthestobjectact), same as NetOxD
x can be film/chip (F), screen/display/picture (P), viewfinder (V), retina (R), etc
NetOxD
Netto On x Deviation [mm or pixel]. This is the same as my MOxD.
x can be film/chip (F), screen/display/picture (P), viewfinder (V), retina (R), etc
When people talk about NetOFD they determine it by:
NetOFD=deviationwinnear - deviationwinfar
with:
deviationwinnear: the deviation of to nearest object relative to the deviation of the stereo window [mm or pixel]
deviationwinfar: the deviation of to farthest object relative to the deviation of the stereo window [mm or pixel]
A deviationwin in front of stereo window is negative, while behind it it is positive.
nonstereooverlap
non stereo overlap on film/chip/screen [mm or pixel] at the stereo window (is normally cropped away).
OxD
The actual On x Deviation [mm or pixel] (due to a certain homologous distant point and farthestobjectact point). Save as deviation
x can be film/chip (F), screen/display/picture (P), viewfinder (V), retina (R), etc
OOxD Optimum On x Deviation [mm or pixel] (related to an optimum experienced parallax angle [parallaxopt~1.9°])
x can be film/chip (F), screen/display/picture (S), viewfinder (V), retina (R), etc.
parallax
parallax angle due to different standpoints (like due to eye separation or stereo base) for a certain point in a 3D scene [°] (Ferwerda [1990], page 237)
Parallax can be an angle in the horizontal of vertical plane (or a combination of the two, thus like a vector in a 3D scene).
parallaxopt
optimum parallax angle of 1.9 [°] for instance due to a 2 m nearest object, farthest object at infinite and a standpoint difference of 65.5 [mm]
picture
is a 2D representation of the real/virtual 3D scene.
Q
a factor between filmwidth and deviation [-]
homologous separation
The distance between homologous points in the two pictures of the stereo pair [mm or pixel].
shifting
Shifting the pictures of the stereo pair in horizontal or vertical direction relative from each other [mm or pixel] (the horizontal shifting changes the experienced stereo depth of the stereo window).
(some people call this parallax [mm or pixel], this is confusing, because the shifting has nothing to do with parallax [aka. different angles])
stereo depth
The distance between nearest and farthest object [mm] in actual life or experienced image
stereo pair
consists of two pictures taken from different viewpoint (distance between viewpoints is stereo base)
stereo window
the (2D) plane of the 3D image that is experienced at the same depth as the display screen (display, projector screen, paper, frame, etc.). At this plane there is normally a 100% stereo overlap for the objects that are at that particular depth.
If the homologous separation of certain points is the same as the frame separation, the stereo window is at the frame plane.
Another glossary site is here <not functional at this moment, but it was a good one>  and the one of ISU <this one is not really consitent enough for me, that si why I made the above one>.

Relations between photographic (stereo) parameters

Relations between stereo parameters

The diagram gives an idea of the relations between photographic (stereo) parameters.
So for instance the stereo base (b0) is determined by the MOFD (Max On Film deviation), the Film to lens distance (a'c), the actual nearest and furthest object distances (and if one wants to utilize the Davis correction [in case furthest distance is smaller then 2 times the nearest distance], although I think one needs to change experienced nearest and furthest object distances instead).
Furthermore one can see that the stereo base (b0)  is used for determining the nonstereo overlap, convergence distance and number of depth steps. By changing e.g. MOFD (through changing experienced nearest object distance), the number of depth steps will also change.

The color codes have the following meaning:

Overview of rules/guidelines and their conditions

The meaning of the condition color coding (and rules/guidelines as a result of the conditions):




Rule/guideline
Condition
farthestobjectact
<=2*nearestobjectact
farthestobjectact>
100*nearestobjectact
deviation
=Fc/30
deviation
=a'c/30
deviation
=1
deviation
=1.2
b0/nearestobjectact=
1/30
25<=
Filmwidth/MOFD
<=35
Filmwidth/MOFD
=30
Fc<<
2*nearestobjectact
Fc
=35
Stereo base
Bercovitz Case 1











Di Marzio1


X








Di Marzio2


X







Di Marzio3 X


X







Sekitani









X

Herbig

X


X




X

Reijs











Deviation
Ferwerda

X




X



X
Di Marzio4

X




X





Di Marzio5
X




X


X

Non stereo overlap
DrT

X







X

Ferwerda

X




X


X

Miscellaneous
Lopp

X



X





ISU
X






X


PKK

X





X

X


Below the formulas and guidelines are given for stereo photography (not for stereo macro stereophotography).

Stereo base

Bercovitz's stereo base formula

Case 1 of Bercovitz
b0=deviation/(farthestobjectact-nearestobjectact)*(farthestobjectact*nearestobjectact/Fc - (farthestobjectact+nearestobjectact)/2)

Di Marzio1's stereo base formula

Case 1 of Bercovitz
take: deviation=Fc/30
b0=DH/60 (The Di Marzio equation for stereography, Frank Di Marzio, 2005, page 3)

Di Marzio2's stereo base formula

Eqn 1 of Bercovitz:
take: m=farthestobjectact/nearestobjectact and m>=2
b0=deviation*nearestobjectact*m/(m-1)/a'c
take: deviation=a'c/30
b0=nearestobjectact*m/(m-1)/30 (The Di Marzio equation for stereography, Frank Di Marzio, 2005, page 19)

Di Marzio3's stereo base formula

Eqn 1 of Bercovitz
assume: farthestobjectact<=2*nearestobjectact (shallow objects)
take: farthestobjectact=2*nearestobjectact (David's condition)
take: deviation=a'c/30
b0=nearestobjectact/15 (The Di Marzio equation for stereography, Frank Di Marzio, 2005, page 14)

Sekitani's stereo base calculator formula

Case 1 of Bercovitz:
take: Fc<<2*nearestobjectact
b0=deviation*nearestobjectact* farthestobjectact/ Fc/( farthestobjectact - nearestobjectact)

Herbig's stereo base guideline

Case 2 of Bercovitz (farthestobjectact>100*nearestobjectact)
take: Fc<<2*nearestobjectact
b0=deviation*nearestobjectact/Fc
take: deviation = 1 mm (which is close to the OOFD=1.2 mm as used with 36*24 mm film)
b0=nearestobjectact/Fc

Reijs' stereo base and deviation formula

Case 1 of Bercovitz:
As much as possible is open, including the deviation (although that one is coupled to the deviation seen on the retina)
The deviation can vary considerable because the human eye can cater for a large parralax range for proper stereo viewing; between LAOFD and HAOFD.

To visualize this rule for a particular configuration (just as an example):
Case 2 of Bercovitz: (farthestobjectact>100*nearestobjectact)
take: Fc<<2*nearestobjectact
deviation= Fc*b0/nearestobjectact
take: b0/nearestobjectact=tan(parallax)
deviation(=MOFD)= Fc*tan(parallax)
guideline: Q=filmwidth/MOFD and filmwidth is cropped filmwidth without non-stereo overlap
Q=filmwidth/Fc/tan(parallax)
tan(parallax)=filmwidth/Fc/Q
take: filmwidth = 36 mm
Looking at a parallax between 1 and 4 degrees (related to LAOFD and HAOFD) gives a more or less comfortable/allowable in stereo viewing. So the greenish areas in the below picture (and even the yellowy area, although in that area less stereo is experienced)) provides a space that provides stereo experience in an allowable form. The below picture if for a 35 mm camera (but equivalent Fc can be found for other [digital] cameras).

VR's guideline
See also this page

Deviation

Ferwerda's deviation guideline

Case 2 of Bercovitz: (farthestobjectact>100*nearestobjectact)
take: b0/nearestobjectact=1/30
take:  Fc=35 mm
deviation(=OOFD)=1.2 mm (for 5-P: 23 mm chip)

Di Marzio4's base deviation guideline

Case 2 of Bercovitz: (farthestobjectact>100*nearestobjectact)
b0=deviation*nearestobjectact/a'c
deviation=a'c*b0/nearestobjectact
take: b0/nearestobjectact=1/30
deviationbase=a'c/30 (he multiplies deviationbase with a Correction Factor [CF] depending on viewing method)

Di Marzio5's base deviation guideline

Case 2 of Bercovitz: (farthestobjectact>100*nearestobjectact)
take: Fc<<2*nearestobjectact
b0=deviation*nearestobjectact/Fc
deviation=Fc*b0/nearestobjectact
take: b0/nearestobjectact=1/30
deviationbase=Fc/30 (he multiplies deviationbase with a Correction Factor [CF] depending on viewing method)

Non stereo overlap

DrT's non stereo overlap formula

Case 2 of Bercovitz: (farthestobjectact>100*nearestobjectact)
take: Fc<<2*nearestobjectact
nonstereooverlap(=deviation)= Fc*b0/nearestobjectac (nonoverlap=FB/I)

Ferwerda's non stereo overlap guideline

Case 2 of Bercovitz: (farthestobjectact>100*nearestobjectact)
take: Fc<<2*nearestobjectact
nonstereooverlap(=deviation)= Fc*b0/ nearestobjectact
take: b0/ nearestobjectact=1/30
nonstereooverlap= Fc/30

Miscellaneous

Lopp's b0/nearestobject guideline

Case 2 of Bercovitz: (farthestobjectact>100*nearestobjectact)
take: deviation(=OOFD)=1.2 mm (as used with 5-P, 7-P or 8-P [36*24 mm] film)

Fc b0/nearestobjectact
35
1/30
50
1/40
74
1/64
135
1/116

ISU guideline

filmwidth/MOFD=30

PKK guideline

Q=croppedfilmwith/MOFD
35>=Q>=25

To visualize this rule for a particular configuration (just as an example)
Case 2 of Bercovitz: (farthestobjectact>100*nearestobjectact)
take: Fc<<2*nearestobjectact
deviation= Fc*b0/nearestobjectact
take: b0/nearestobjectact=tan(parallax)
deviation(=MOFD)= Fc*tan(parallax)
guideline: Q=croppedfilmwidth/MOFD and cropped filmwidth is without non-stereo overlap
Q=croppedfilmwidth/Fc/tan(parallax)
tan(parallax)=croppedfilmwidth/Fc/Q
take: croppedfilmwidth = 36 mm

The Q is checked realtime in the viewfinder. Keeping Q between 25 and 35 by moving around the camera (by changing Fc, b0 and/or nearest/farthestobjectact), this guideline can work because it utilizes the flexibility of the parallax that can be experienced by the eye/brain combination (blue rectangular in below picture, which is superimposed on Reijs' guidelines).

Reijs' evaluation of above guidelines

In a lot of guidelines/formulas; the factor 1/30 pops up which is in my opinion related to tan(parallaxopt) and parallaxopt = 1.9 degrees (pink line in below picture).
Looking at a parallax between 1 and 4 degrees (related to LAOFD and HAOFD) gives a more or less comfortable/allowable in stereo viewing. So the greenish areas in the below picture (and even the yellowy area, although in that area less stereo is experienced)) provides a space that provides stereo experience in an allowable form.

PKK's guideline

Most of the other guidelines are based on a fixed parallax angle of 1.9° (pink line: parallaxopt), so these guidelines find one line in that space. The PKK guideline (the blue rectangle) utilizes already more flexibility of the parallax angle, but the stereo experience allows for a larger space, as proposed in Reijs' stereobase.

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Major content related changes: May 18, 2005