Re: "Full-spectrum" article on Wikipedia

On Tue, 05 Jun 2007 20:14:44 -0400, Victor Roberts
<xxx@xxxxxxxxxxxxxxxxxxxxx> wrote:

On Wed, 6 Jun 2007 00:39:58 +0300, "Ioannis"
<morpheus@xxxxxxxxxxxx> wrote:

"Victor Roberts" <xxx@xxxxxxxxxxxxxxxxxxxxx> wrote in message
news:avjb63h91aafttkq0b9p260ps600euk699@xxxxxxxxxx
[snip]

Your formula seems correct. How far off are your
calculations? can you post a couple of results?

Except for incandescent lamps, I don't see that Table 1 of
the LRC publications gives you enough information about the
spectrum of the lamps in question to make an accurate
calculation.

Vic,

here's what I used and what I've got:

I've used:

FSI = sum((1 - i_k/i_max)^2, k=380..700)/(700-380), where i_max is the
maximum on the measured spectrum and i_k is the intensity at
wavelength k. I've gone only as far as 700, since I don't use the
additional 30nms.

Here's what I've got for my lamps, using the same abbreviation as on
my Engineering document, with the rating in parens:

TH 0.312 (2)
D 0.024 (1)
CFL27K 0.98 (10)
CFL4K 0.965 (7)
HPM 0.988 (14)
HPMC 0.983 (11)
BL 0.974 (9)
MHE 0.987 (13)
MHA 0.968 (8)
MHD 0.974 (9)
PLANT 0.984 (12)
BLAU 0.991 (15)
GRUN 0.995 (16)
DIAZ1 0.949 (5)
DIAZ2 0.996 (17)
LPS 0.997 (18)
HPS 0.922 (4)
FLASH 0.858 (3)
HPX 0.963 (6)

In general the ordering appears consistent. In my opinion two lamps
are dissonant: HPS and HPX. HPS should not be that high in the list
and HPX should be higher. The HPS discrepancy can be explained: It's
probably my approximation of the spectrum using Lorenztians which
gives too much attention to the D wings, thus filling the spectrum
some. The HPX is also somewhat faulty, as it was gotten by balancing
Becker's online spectrum, and the red component is too strong.
Otherwise the number gives roughly the percentage of how "empty" the
spectrum is.

A second comment on the HPS: If one increases the pressure some more,
one gets a 2500K HPS "white" sodium lamp, which is close to an
incandescent, so perhaps the calculation for the HPS is not that
faulty afterall. I don't know.

I am not sure whether I will pursue this avenue yet, because otherwise
my spectra ARE balanced, and I don't want to do guesswork with the FSI
formula. If the authors wanted this to be a serious calculation they
should have included the exact mathematical formula used.

Ioannis,

I've been distracted the past couple of days and now believe
I didn't respond correctly in my previous note, and
responded before I had reviewed the LRC paper in detail.

Your formula seems to sum the squares of the differences
between the lamp spectrum and the flat spectrum at each
wavelength. Is that correct? (This is how I first thought
the LRC was calculating the FSI.) If so, I now believe your
formula is incorrect.

Upon further review of the LRC paper it now seems that they
first calculate what they call the "cumulative SPD" for a
given lamp and then calculate the squares of the differences
between that cumulative SPD and a linear line that
represents the flat reference spectrum.

I'm going to use the cumulative SPD method to calculate the
FSI for blackbodies of various temperatures and get back to
you here.

I just calculated the FSI of a 2700 K blackbody using the
formula proposed by the LRC to the best of my understanding.
I get a value of 16.7, vs the LRC's value of 5.3 for 40 to
100 watt incandescent lamps. While an incandescent lamp is
not exactly a blackbody, it is close enough that my
calculations should not have differed this much from the
LRC's numbers if I was doing the calculation correctly.

I'll call Conan O'Rourke at the LRC tomorrow and try to
figure this out.

--
Vic Roberts
http://www.RobertsResearchInc.com
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Relevant Pages

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