Reply #17 - April 13, 2007, 09:00:06 PM
signal goes through multitude of electronic stages, the
more relevant being the video gain, the white balance and
the parameters (gain and offset) of the analog-to-digital
converter (ADC). These parameters can influence a
posteriori the raw opto-electronic conversion and, because
they are built-in parameters, we may denote them as the
intrinsic parameters of a digital camera (Fig. 1).
Nevertheless, these intrinsic parameters, all of them of
electronic type, can be numerous and then they require
careful control. For example, if video gain is selected by
control menu in automatic mode, we lose control of the
global generation process of the digital output from the
radiometric input, because the digital image capture device
will change freely this process. This means that, if we wish
to calibrate the device, we must use a characterization
model for each video gain value because, with a fixed
radiometric input, the device gives different output data.
This prevents for instance the determination of the raw
RGB color space associated to the spectral sensitivities of
the digital camera.
The Reciprocity Law in Digital Photography
From the former discussion, the key to control the
input-output process in a digital camera is to know and to
control all the sub-processes that play a role before, during
and after the raw opto-electronic conversion. For example,
independently of the choice of extrinsic and intrinsic
parameters, the incident photon rate1,2 nν(λ) on the image
sensor in direct angle incidence in an electronic or digital
still picture camera is:
( ) ( )
( )
τ (λ) (λ)
+
ν λ = π λ λ 2 LENS ATM
LENS
2
SENSOR
4 1 '
T
N m
L A t
hc
n e (1)
where λ is wavelength, h is Planck's constant, c is the
speed of light in the medium, Le(λ) is the spectral radiance
of the object or target, ASENSOR is the effective or irradiated
sensor area, t is the photosite integration time of the
shutter, N is the f-number of the zoom-lens, m'LENS is the
lateral magnification of the zoom-lens, τLENS(λ) is the
spectral transmittance of the zoom-lens and TATM(λ) is the
spectral transmittance of the atmosphere.
Thus, the spectral exposure H(λ) is expressed as:
( ) (λ)
λ
λ = nν
hc
H (2)
The simplest way to understand the opto-electronic
conversion that takes place in a digital still camera is to
express the spectral exposure H(λ) as proportional to the
spectral radiance Le(λ) of the target and to the photosite
integration time t, and inversely proportional to the square
of the f-number N. If we take into account that spectral
transmittance of the atmosphere ΤATM(λ) in the visible
range is one and that, for most zoom-lenses, spectral
transmittance τLENS(λ) is approximately constant in the
visible range with a value also close to one, the previous
expression becomes:
( ) ( )
( ) 2 LENS ATM
LENS
SENSOR
2 4 1 '
, T
m
A
t k
N
L
H k e τ
+
λ = λ = π (3)
From Eq. (3) and independently of considering
exposure processes with spectral or gray scale patterns, it
seems that different combinations of spectral radiance
Le(λ), f-number N and photosite integration or exposure
time t will provide equivalent exposures with identical
camera responses. If the spectral exposures are equal, H1(λ)
= H2(λ), then, according to Eq. 3:
2
1
2
1
2
2 1 ,
t
t
N
N
m L m L e e
= ⋅ = (4)
Note than, whereas for m equal to one the values of
radiance that yield equal exposures will be equal
(equivalent exposure series), for m ≠ 1 the values will be
different (non equivalent exposure series).
This argumentation is known as reciprocity law, either
in Photochemical (classical) or Digital Photography. Even
though it seems well established historically that AgX3-7
and other photosensible8 materials present some deviations
from this law, it is still to be determined whether or not the
same law holds in the image sensors of digital cameras.
Although concerned with the shutter in the image capture,
the ISO 516 normative9 has been devised by the WG4
(Mechanical Elements for Photography), and not the
WG18 (Electronic Still Picture Imaging). Therefore, it is
basically a revision of the ISO 516:1986 standard applied
to the electro-mechanical shutters, and not for the
electronically shuttered sensors, which are coupled to the
image sensor and are the most widely used at present.
There is no reference in the current ISO norms to the
reciprocity law problem in Digital Photography, which
implicitly assume that this law is not verified under any
circumstance. This is valid too for the ISO 14524
normative10 because the opto-electronic conversion
functions (OECFs) associated to different N or t values are
not equivalent. Although it is well established that the
reciprocity law does not hold with white light, maybe it is
verified using monochromatic light. So, it is valid to
extrapolate the OECF concept to OECSF (opto-electronic
conversion spectral function) as the starting point of the
study of the applicability of the reciprocity law in Digital
Photography.
Experimental Set-Up
Figure 2 shows the experimental set-up, which can also be
used to obtain the spectral sensitivities11 of any camera.
Light coming from a broadband light source (LS, Osram
HQI T 250 W Daylight Hg vapor fluorescent lamp) passes
through a monochromator (MC, CVIS Laser Digikröm
DK240) to produce a monochromatic target over the opal
glass (OG). The target radiance Le(λ) was measured by a
tele-spectroradiometer (TSRM, Photo Research PR-650
SpectraColorimeter) that could be removed to allow the
IS&T's 2003 PICS Conference
513 More to come....
Logged
Ed Shapiro
The Hintonburg Studio
Suite 201 78 Hinton Avenue North
Ottawa, Ontario CANADA K1Y 0Z8
613-792-4837 Email:
edshapiro@rogers.com
:
)
