uses of SQM and how to re-calibrate

[Jan Hollan <jhollan@amper....muni.cz>]

To the issue raised by Jim and commented upon by David and Doug:

                 General photometry with the SQM

SQM can be employed as it is, with its default calibration, or it can be
productively used in alternative ways. Alternatives demand subsequent
calibration. I'll describe them somewhat; the same would apply to any
light sensor.

SQM default calibration is, in my guess, made in such a way, that it is
pointed toward a scene with a uniform luminance, ideally observing the
interior of an integrating sphere. Thanks to the negligible sensitivity of
SQM behind 80 degrees, an outdoor uniform wall lit by clouds may be a good
replacement for the integrating sphere; however, even for a luxmeter,
these areas should add but 3 per cent, so it can be OK too.


Checking a base calibration, if you have a luxmeter:

If a luxmeter is pointed to the wall (some 2 dm from it, to dilute its
shadow), its reading divided by ``one pi steradians'' is the luminance of
the wall (the same holds for an integrating sphere, of course).

If almost 6 sr of uniform luminance are not available, a smaller space
angle can be measured. Make an opening in a large black box and limit the
cone visible to the luxmeter to some 30 degrees, so that it's ``cosine
correction'', which is never perfect, becomes irrelevant, then the reading
of luxmeter divided by the visible space angle is the luminance.

How large is that space angle? I have to admit I was surprised, how small
is the difference of the correct formula for space angle (obtained by
integrating 2pi*sin(radius)) from its planar approximation pi*r^2 (used by
Jim). To visualise that, I've made two gnuplot scripts, their outputs are
available within
 http://amper.ped.muni.cz/light/luminance/sqm/space_angle/
or zipped in its parent directory.


Calibration for alternative uses:

1) when any filter is added (including a white dispersing piece, to
cosine-correct the SQM roughly), and

2) when the angular aperture is changed from the initial full semi-space
(observing through an opening in a black box, with a reproducible position
of SQM with respect to it)

Calibration consists simply by taking two readings, with original SQM and
with adapted one. That with the adapted is larger (meaning less light).
Original-adapted is a negative number, which is to be added to adapted
readings, so that they would again mean, how many magnitudes has a square
second of a uniformly bright scene. Calibration is easy to do with any
uniformly lit wall or snow (outdoors, by clouds).

SQM can be employed as an extremely sensitive luxmeter to measure
illuminance by a distant lamp or by moon. This task is however different
from measuring a scene of almost uniform luminance. SQM should be pointed
directly to the source. Then it receives radiation with its maximum
sensitivity, and minor departures (10 degrees) from this direction play
hardly any role.

In principle, no new calibration should be needed for this purpose: The
result, ``apparent luminance'' could be simply multiplied by the published
effective aperture of SQM, 1.53 sr, to get illuminance (or, what is the
same, luminous flux density from the investigated light source). In my
experience, this is not satisfying, however. ``My'' SQM differs from the
published instrument test by having an effective aperture of about 1.9 sr
(apart from reporting about 0.1 mag more than measured by a luxmeter, for
uniform luminance, what is to be expected perhaps for most types of
light). I get good point-source luminous flux densities using
             22E4 * 10^(-0.4*reading) lm/m2.

So, Jim's proposal is almost OK, just the factor to be used is not 1 sr,
but by the instrument's effective space angle aperture: some 1.5 sr, or
perhaps up to whole 2 steradians for some SQMs (easy to check using any
luxmeter). Tiny changes in the position of the sensor within the
instrument, perhaps even the varying properties of the sensors, are a
probable cause of this varying effective space angle aperture, the
knowledge of which is needed for point-source measurements.


Point-source measurement:

In a typical situation there is some ambient light in addition to the
direct light from the single source ahead of the instrument. If just that
light coming along the axis of the SQM sensor is to be measured, two
readings are needed: the auxiliary one is to be made when casting a shadow
onto the detector. The readings can to be converted to luminances (cd/m2)
in a default recommended way
  ( 10.8E4 * 10^(-0.4*reading) cd/m2 ),
 the shadow value subtracted from the full light one, and _for my SQM_,
the resulting ``direct-light equivalent luminance'' multiplied by 2
(steradians) to get direct light (or ``paraxial'') illuminance.


Finding the conversion factor for _your_ SQM:

You can find the effective space angle aperture of your SQM even without
any luxmeter. Just observe a uniform wall through an opening with an
angular diameter of max. 20 degrees. If the opening diameter would be
10 cm, and the distance of the sensor from it would be 30 cm, then the
angular radius of the opening would be 1/6 rad and the space angle would
be 0.087 sr. Thanks to the fact, that sensitivity of the SQM is almost
constant within this angle, it is also the effective space angle at this
configuration.

If the reading through such opening and a reading taken without any
obstacle would differ by 3.10 (mag), it would mean that the effective
space angle of unobstructed SQM is 17.4 times larger, or 1.51 sr. If the
readings would differ by 3.30, the effective space angle of unobstructed
SQM would be implied as 1.82 sr.


Measuring sky luminances in zenith:

I assume that it would not be difficult to make an adapter which would
limit SQM total aperture to a cone with 30 degrees radius (i.e., having
0.84 sr space angle). It would reduce the light gain of the instrument to
about one half. Something very close to zenith luminance would be directly
measured this way (subtracting the constant appropriate for this
configuration, as found by measuring a uniform wall), with a further
advantage that such a cone can be obtained almost everywhere, even among
buildings etc. And still other advantage, that differing sensitivities of
various SQMs at 60+ degrees, which may confuse the results due to
much brighter sky above horizon, would cease to have any influence.


Conclusion:

SQM is a wonderful, extremely sensitive instrument for many possible uses.
Rely on its base calibration and make the derived needed ones for its
alternative uses. If you get a lot of interesting measurements, there is
always a possibility to make some repeated calibrations with luxmeters (or
even spot luminance meters), for various situations where SQM has been
employed, to get somewhat better accuracy and to be able to present your
results to any lighting expert with enough self-confidence.

(by the way, with a proper opening, SQM may become an accurate exposimeter
for night photography).

cheers,
 jenik