Calibration of sensor.. need help

Post by Faraz Arshad
Dear All,
During last few months I had been struggling with different concepts
in color systems. Actually I am designing a color sensor for liquids
for my project and being an engineer I have lots of difficulties
tackling some mathematical issues.
Lately I have encountered a problem. For calibration of my sensor on
different industrial regulations I read the regulation on Rosin color
scale D509 and wanted to implement it. Now the point is that you know
the path length of fluid affects the color in general. The longer the
path length containing solution the darker would be the appearance.
Now I have the values of xyY (chromaticity coordinates) for 22.6mm
path length. If I want to get the values for 10mm path length by doing
some maths I know that the values of spectral reflectance Y would
change as per Beers law and should look like Y^(10/22.6). But the
question is that how do I get to the new xy values after calculating
the new Y under 10mm path length. Is there a mathematical way. I know
that x=(X)/X+Y+Z, but could we solve this equation to get corrected
xy. And secondly am I even right about the fact that changing path
length should change xy and not only Y.
Please help me, I am screwed by this.
Best
Faraz

Ideally, the chromaticity coordinates x,y don't depend on the path
length.
The spectral transmission or absorbance spectra are scaled by the
path length. The scale factor cancels in the calculations x=X/(X+Y+Z)
and so on.
Much recommended (also concerning discussions about deviations from
the ideal case):
Roy S.Berns
Billmeyer and Saltzman's Principles of Color Technology
Third edition

Best regards --Gernot Hoffmann

Erik Nikkanen

2010-05-05 21:08:54 UTC

Ideally, the chromaticity coordinates x,y don't depend on the path
length.
The spectral transmission or absorbance spectra are scaled by the
path length. The scale factor cancels in the calculations x=X/(X+Y+Z)
and so on.
Much recommended (also concerning discussions about deviations from
Roy S.Berns
Billmeyer and Saltzman's Principles of Color Technology
Third edition
Best regards --Gernot Hoffmann

I might not be correctly understanding the question and conditions and this
answer, but it does not seem correct.

In dealing with the reflection of ink films, the thickness of the ink film
could be considered as the path in the above question. (I think)

As an ink film increases, the shape of the spectral curve does not change in
a scaled way relative to the zero reflectance line of a plot. The relative
shape of the spectral curve changes and there will be a hue shift due to
that change. This is because the light that in being removed due the
thicker ink film is scaled from the top down of a 0 to 1 reflectance plot.
For a specific spectral curve, the increase of ink film scales downwards
from the initial curve plot. Not sure if that is clear. The resulting
colour shift is determined from the 0 level up, which represents the
remaining reflected light along the curve.

This is how I understand it and have observed it. Maybe inks are a little
different since they are semitransparent but I don't think so.

Erik

Erik Nikkanen

2010-05-05 21:24:48 UTC

Ideally, the chromaticity coordinates x,y don't depend on the path
length.
The spectral transmission or absorbance spectra are scaled by the
path length. The scale factor cancels in the calculations x=X/(X+Y+Z)
and so on.
Much recommended (also concerning discussions about deviations from
Roy S.Berns
Billmeyer and Saltzman's Principles of Color Technology
Third edition
Best regards --Gernot Hoffmann

I might not be correctly understanding the question and conditions and this
answer, but it does not seem correct.
In dealing with the reflection of ink films, the thickness of the ink film
could be considered as the path in the above question. (I think)
As an ink film increases, the shape of the spectral curve does not change in
a scaled way relative to the zero reflectance line of a plot. The relative
shape of the spectral curve changes and there will be a hue shift due to
that change. This is because the light that in being removed due the
thicker ink film is scaled from the top down of a 0 to 1 reflectance plot.
For a specific spectral curve, the increase of ink film scales downwards
from the initial curve plot. Not sure if that is clear. The resulting
colour shift is determined from the 0 level up, which represents the
remaining reflected light along the curve.
This is how I understand it and have observed it. Maybe inks are a little
different since they are semitransparent but I don't think so.
Erik

I have to add that the scaling down is not by the same percentage along the
curve but depends on the amount of filtering affect at each point along the
curve. Erik

Gernot Hoffmann

2010-05-06 05:37:31 UTC

Ideally, the chromaticity coordinates x,y don't depend on the path
length.
The spectral transmission or absorbance spectra are scaled by the
path length. The scale factor cancels in the calculations x=X/(X+Y+Z)
and so on.
Much recommended (also concerning discussions about deviations from
Roy S.Berns
Billmeyer and Saltzman's Principles of Color Technology
Third edition
Best regards --Gernot Hoffmann

I might not be correctly understanding the question and conditions and

this

Post by Erik Nikkanen
answer, but it does not seem correct.
In dealing with the reflection of ink films, the thickness of the ink

film

Post by Erik Nikkanen
could be considered as the path in the above question. (I think)
As an ink film increases, the shape of the spectral curve does not change

Post by Erik Nikkanen
a scaled way relative to the zero reflectance line of a plot. The

relative

Post by Erik Nikkanen
shape of the spectral curve changes and there will be a hue shift due to
that change. This is because the light that in being removed due the
thicker ink film is scaled from the top down of a 0 to 1 reflectance plot.
For a specific spectral curve, the increase of ink film scales downwards
from the initial curve plot. Not sure if that is clear. The resulting
colour shift is determined from the 0 level up, which represents the
remaining reflected light along the curve.
This is how I understand it and have observed it. Maybe inks are a little
different since they are semitransparent but I don't think so.
Erik

I have to add that the scaling down is not by the same percentage along the
curve but depends on the amount of filtering affect at each point along the
curve. Erik

Erik Nikkanen

2010-05-06 13:52:01 UTC

Ideally, the chromaticity coordinates x,y don't depend on the path
length.
The spectral transmission or absorbance spectra are scaled by the
path length. The scale factor cancels in the calculations x=X/(X+Y+Z)
and so on.
Much recommended (also concerning discussions about deviations from
Roy S.Berns
Billmeyer and Saltzman's Principles of Color Technology
Third edition
Best regards --Gernot Hoffmann

I might not be correctly understanding the question and conditions and

this

Post by Erik Nikkanen
answer, but it does not seem correct.
In dealing with the reflection of ink films, the thickness of the ink

film

Post by Erik Nikkanen
could be considered as the path in the above question. (I think)
As an ink film increases, the shape of the spectral curve does not change

Post by Erik Nikkanen
a scaled way relative to the zero reflectance line of a plot. The

relative

little

Post by Erik Nikkanen
different since they are semitransparent but I don't think so.
Erik

I have to add that the scaling down is not by the same percentage along the
curve but depends on the amount of filtering affect at each point along the
curve. Erik

Erik,

the Boguer-Beer / Beer-Lambert law is valid under certain assumptions,
therefore I had written 'ideally':
http://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law

It's not valid for ink films on prints.Here, the Kubelk-Munk theory is
more
appropriate.

Best regards --Gernot Hoffmann

Gernot,

I think my modeling was more in line with the Beer-Lambert law. Along the
spectral curve, different rates of absorbtion are experienced and this in
turn changes the relative shape of the spectral curve. This then results in
a hue shift.

My view is that if one changes the intensity of the illumination going into
the path, then the spectral curve woud change proportionally and therefore
no change in hue, just L. But the spectral curve after the absorbtion
throught different path lengths would change the spectral curve in a non
proportional way due to the different amounts of absorption at different
wave lengths along the curve and therefore changing the hue.

Since I am not a colour scientist, so I will not defend my view ( because it
could be wrong :-) ) but it would be interesting to see if Faraz has some
experimental data to support or not support a change in hue when he
increases the path.

I am surprised that I have posted here after such a long time. That
question just sparked an area of interest. I think I shall stop here before
I get burned due to my colour science ignorance. ;-) Erik

Gernot Hoffmann

2010-05-06 13:39:07 UTC

Post by Faraz Arshad

color

Post by Faraz Arshad
scale D509 and wanted to implement it. Now the point is that you

know

Post by Faraz Arshad
the path length of fluid affects the color in general. The longer

the

Post by Faraz Arshad
path length containing solution the darker would be the appearance.
Now I have the values of xyY (chromaticity coordinates) for 22.6mm
path length. If I want to get the values for 10mm path length by

doing

Post by Faraz Arshad
some maths I know that the values of spectral reflectance Y would
change as per Beers law and should look like Y^(10/22.6). But the
question is that how do I get to the new xy values after calculating
the new Y under 10mm path length. Is there a mathematical way. I

know

Post by Faraz Arshad
that x=(X)/X+Y+Z, but could we solve this equation to get corrected
xy. And secondly am I even right about the fact that changing path
length should change xy and not only Y.
Please help me, I am screwed by this.
Best
Faraz

Ideally, the chromaticity coordinates x,y don't depend on the path
length.
The spectral transmission or absorbance spectra are scaled by the
path length. The scale factor cancels in the calculations x=X/(X+Y+Z)
and so on.
Much recommended (also concerning discussions about deviations from
Roy S.Berns
Billmeyer and Saltzman's Principles of Color Technology
Third edition
Best regards --Gernot Hoffmann

I might not be correctly understanding the question and conditions and

this

Post by Erik Nikkanen
answer, but it does not seem correct.
In dealing with the reflection of ink films, the thickness of the ink

film

Post by Erik Nikkanen
could be considered as the path in the above question. (I think)
As an ink film increases, the shape of the spectral curve does not

change

Post by Erik Nikkanen
in

Post by Erik Nikkanen
a scaled way relative to the zero reflectance line of a plot. The

relative

plot.

Post by Erik Nikkanen
For a specific spectral curve, the increase of ink film scales downwards
from the initial curve plot. Not sure if that is clear. The resulting
colour shift is determined from the 0 level up, which represents the
remaining reflected light along the curve.
This is how I understand it and have observed it. Maybe inks are a

little

Post by Erik Nikkanen
different since they are semitransparent but I don't think so.
Erik

I have to add that the scaling down is not by the same percentage along

the

Post by Erik Nikkanen
curve but depends on the amount of filtering affect at each point along

the

Post by Erik Nikkanen
curve. Erik

Erik,
the Boguer-Beer / Beer-Lambert law is valid under certain assumptions,
therefore I had written 'ideally':http://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law
It's not valid for ink films on prints.Here, the Kubelk-Munk theory is
more
appropriate.
Best regards --Gernot Hoffmann
Gernot,
I think my modeling was more in line with the Beer-Lambert law. Along the
spectral curve, different rates of absorbtion are experienced and this in
turn changes the relative shape of the spectral curve. This then results in
a hue shift.
My view is that if one changes the intensity of the illumination going into
the path, then the spectral curve woud change proportionally and therefore
no change in hue, just L. But the spectral curve after the absorbtion
throught different path lengths would change the spectral curve in a non
proportional way due to the different amounts of absorption at different
wave lengths along the curve and therefore changing the hue.
Since I am not a colour scientist, so I will not defend my view ( because it
could be wrong :-) ) but it would be interesting to see if Faraz has some
experimental data to support or not support a change in hue when he
increases the path.
I am surprised that I have posted here after such a long time. That
question just sparked an area of interest. I think I shall stop here before
I get burned due to my colour science ignorance. ;-) Erik

Erik,

nice to meet you here again. Unfortunately, this forum is almost dead.

Concerning Beer-Lambert I don't have practical experience. I'm
referring
only to the book by Berns. Here we find examples of normalized
spectra for different path lengths. The normalized spectra are almost
identical, which tells us that the Beer-Lambert law is valid in this
case.
You are probably right, assuming that this law cannot be applied in
many cases. For instance: what happens if the fluid is a pigment
ink instead of solvent ink?

Best regards --Gernot Hoffmann

Gernot Hoffmann

2010-05-07 15:49:20 UTC

Post by Faraz Arshad

color

Post by Faraz Arshad
scale D509 and wanted to implement it. Now the point is that you

know

Post by Faraz Arshad
the path length of fluid affects the color in general. The longer

the

doing

know

Ideally, the chromaticity coordinates x,y don't depend on the path
length.
The spectral transmission or absorbance spectra are scaled by the
path length. The scale factor cancels in the calculations x=X/(X+Y+Z)
and so on.
Much recommended (also concerning discussions about deviations from
Roy S.Berns
Billmeyer and Saltzman's Principles of Color Technology
Third edition
Best regards --Gernot Hoffmann

I might not be correctly understanding the question and conditions and

this

Post by Erik Nikkanen
answer, but it does not seem correct.
In dealing with the reflection of ink films, the thickness of the ink

film

Post by Erik Nikkanen
could be considered as the path in the above question. (I think)
As an ink film increases, the shape of the spectral curve does not

change

Post by Erik Nikkanen
in

Post by Erik Nikkanen
a scaled way relative to the zero reflectance line of a plot. The

relative

plot.

little

Post by Erik Nikkanen
different since they are semitransparent but I don't think so.
Erik

I have to add that the scaling down is not by the same percentage along

the

Post by Erik Nikkanen
curve but depends on the amount of filtering affect at each point along

the

Post by Erik Nikkanen
curve. Erik

Erik,
the Boguer-Beer / Beer-Lambert law is valid under certain assumptions,
therefore I had written 'ideally':http://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law
It's not valid for ink films on prints.Here, the Kubelk-Munk theory is
more
appropriate.
Best regards --Gernot Hoffmann
Gernot,
I think my modeling was more in line with the Beer-Lambert law. Along the
spectral curve, different rates of absorbtion are experienced and this in
turn changes the relative shape of the spectral curve. This then results in
a hue shift.
My view is that if one changes the intensity of the illumination going into
the path, then the spectral curve woud change proportionally and therefore
no change in hue, just L. But the spectral curve after the absorbtion
throught different path lengths would change the spectral curve in a non
proportional way due to the different amounts of absorption at different
wave lengths along the curve and therefore changing the hue.
Since I am not a colour scientist, so I will not defend my view ( because it
could be wrong :-) ) but it would be interesting to see if Faraz has some
experimental data to support or not support a change in hue when he
increases the path.
I am surprised that I have posted here after such a long time. That
question just sparked an area of interest. I think I shall stop here before
I get burned due to my colour science ignorance. ;-) Erik

I've deleted my posts because the OP didn't respond.

Best regards --Gernot Hoffmann

Faraz Arshad

2010-05-12 11:28:58 UTC

Post by Faraz Arshad

color

Post by Faraz Arshad
scale D509 and wanted to implement it. Now the point is that you

know

Post by Faraz Arshad
the path length of fluid affects the color in general. The longer

the

doing

know

Ideally, the chromaticity coordinates x,y don't depend on the path
length.
The spectral transmission or absorbance spectra are scaled by the
path length. The scale factor cancels in the calculations x=X/(X+Y+Z)
and so on.
Much recommended (also concerning discussions about deviations from
Roy S.Berns
Billmeyer and Saltzman's Principles of Color Technology
Third edition
Best regards --Gernot Hoffmann

I might not be correctly understanding the question and conditions and

this

Post by Erik Nikkanen
answer, but it does not seem correct.
In dealing with the reflection of ink films, the thickness of the ink

film

Post by Erik Nikkanen
could be considered as the path in the above question. (I think)
As an ink film increases, the shape of the spectral curve does not

change

Post by Erik Nikkanen
in

Post by Erik Nikkanen
a scaled way relative to the zero reflectance line of a plot. The

relative

plot.

little

Post by Erik Nikkanen
different since they are semitransparent but I don't think so.
Erik

I have to add that the scaling down is not by the same percentage along

the

Post by Erik Nikkanen
curve but depends on the amount of filtering affect at each point along

the

Post by Erik Nikkanen
curve. Erik

Erik,
the Boguer-Beer / Beer-Lambert law is valid under certain assumptions,
therefore I had written 'ideally':http://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law
It's not valid for ink films on prints.Here, the Kubelk-Munk theory is
more
appropriate.
Best regards --Gernot Hoffmann
Gernot,
I think my modeling was more in line with the Beer-Lambert law. Along the
spectral curve, different rates of absorbtion are experienced and this in
turn changes the relative shape of the spectral curve. This then results in
a hue shift.
My view is that if one changes the intensity of the illumination going into
the path, then the spectral curve woud change proportionally and therefore
no change in hue, just L. But the spectral curve after the absorbtion
throught different path lengths would change the spectral curve in a non
proportional way due to the different amounts of absorption at different
wave lengths along the curve and therefore changing the hue.
Since I am not a colour scientist, so I will not defend my view ( because it
could be wrong :-) ) but it would be interesting to see if Faraz has some
experimental data to support or not support a change in hue when he
increases the path.
I am surprised that I have posted here after such a long time. That
question just sparked an area of interest. I think I shall stop here before
I get burned due to my colour science ignorance. ;-) Erik

Dear Erik,

Well this is getting tricky. Your suggestion has opened another
question for me. For one of my calibration, I have to prepare samples
by adding some solvent to liquid. For eg 1 gram of solvent in 1 liter
would account for one of the color index, 2 gram in a liter would give
color index thats twice that value. Its on an absolute linear scale.
Now what I have done to make things simple is I have put the 1 g per
liter sample into many cuvettes of the same dimensions, so for 2 g, I
sort of concatenate the two cuvettes and measure the value. Now from
what you have said, it looks like that the concatenation of 2 cuvettes
with 1 gram each shouldnt be EQUAL to one cuvette having 2 gram of
sample. So would this calibration fail. How shall I calibrate
something like this. From what Gernot Hoffman said, calibrating this
way shouldnt change the xy values but only Y since only the path
length keeps on increasing. In reality for samples like these should
the xy values change too.
Need your insights..

Best,
Faraz

Faraz Arshad

2010-05-12 12:26:44 UTC

"But the spectral curve after the absorbtion
throught different path lengths would change the spectral curve in a
non
proportional way due to the different amounts of absorption at
different
wave lengths along the curve and therefore changing the hue."

As you said Erik.

Why wouldnt this happen in the first case, when you are just
increasing intensity. According to Beers Law both situations are
equivalent. I dint get your point. Could you explain further.
Perhaps Gernott could chip in.

Best

Erik Nikkanen

2010-05-12 13:59:57 UTC