Thread Subject: Help needed with Non-Linear Least Square Fitting

Hi Guys,
So I'm measuring Reflectance(v2) vs. Wavelength(v1) and
need to find the thickness of my sample, for that I'm
trying to use fitting to a function using the nonlinear
square method to find couple of unknowns.
If anyone can help please email me at nimakev@yahoo.com so
I'll send you more information,
any help is greatly appericiated.
 
thank you.

"Nima Azar" <nimakev@yahoo.com> wrote in message
<g0i43e$n5i$1@fred.mathworks.com>...
> Hi Guys,
> So I'm measuring Reflectance(v2) vs. Wavelength(v1) and
> need to find the thickness of my sample, for that I'm
> trying to use fitting to a function using the nonlinear
> square method to find couple of unknowns.
> If anyone can help please email me at nimakev@yahoo.com
so
> I'll send you more information,
> any help is greatly appericiated.
>
> thank you.

So Here's the Function:
v2 = -a – b*v1 – c*(v1)^2 + d[1+(e/2d)cos((16.745*g/v1) +
h)] Exp(-j/(v1)^2)

so basically g and h are to be found through fitting...

thanks for helps.

"Nima Azar" <nimakev@yahoo.com> wrote in message <g0i43e$n5i
$1@fred.mathworks.com>...
> Hi Guys,
> So I'm measuring Reflectance(v2) vs. Wavelength(v1) and
> need to find the thickness of my sample, for that I'm
> trying to use fitting to a function using the nonlinear
> square method to find couple of unknowns.
> If anyone can help please email me at nimakev@yahoo.com so
> I'll send you more information,
> any help is greatly appericiated.
>
> thank you.
-------------
  I'm afraid my physics is a little rusty at this point. You need to tell in what way
sample thickness is to depend on reflectance and wavelength in your fitting
model.

Roger Stafford

"Roger Stafford"
<ellieandrogerxyzzy@mindspring.com.invalid> wrote in
message <g0i4o4$2lt$1@fred.mathworks.com>...
> "Nima Azar" <nimakev@yahoo.com> wrote in message
<g0i43e$n5i
> $1@fred.mathworks.com>...
> > Hi Guys,
> > So I'm measuring Reflectance(v2) vs. Wavelength(v1) and
> > need to find the thickness of my sample, for that I'm
> > trying to use fitting to a function using the nonlinear
> > square method to find couple of unknowns.
> > If anyone can help please email me at nimakev@yahoo.com
so
> > I'll send you more information,
> > any help is greatly appericiated.
> >
> > thank you.
> -------------
> I'm afraid my physics is a little rusty at this point.
You need to tell in what way
> sample thickness is to depend on reflectance and
wavelength in your fitting
> model.
>
> Roger Stafford
>

Thanks Roger for your reply:

Here's the Function:
v2 = -a – b*v1 – c*(v1)^2 + d[1+(e/2d)cos((16.745*g/v1) +
h)] Exp(-j/(v1)^2)

so basically g and h are to be found through fitting...and
I can get V1, V2 through measurments...

thanks for help.

"Nima Azar" <nimakev@yahoo.com> wrote in message <g0i5kc$pjn
$1@fred.mathworks.com>...
> Thanks Roger for your reply:
>
> Here's the Function:
> v2 = -a – b*v1 – c*(v1)^2 + d[1+(e/2d)cos((16.745*g/v1) +
> h)] Exp(-j/(v1)^2)
>
> so basically g and h are to be found through fitting...and
> I can get V1, V2 through measurments...
>
> thanks for help.
-------------
  If you have the Optimization Toolbox, one way is to use 'fsolve'.

  In case you don't have that toolbox, I notice that the equation can be
reformulated to look like this:

 A*g+h = B

where A and B are column vectors that depend on the various values of V1
and V2. This is done by solving for the cosine expression in terms of
everything else and then taking the arccosine of both sides. In this form it is
a standard linear least squares problem for which you can use matlab's
backslash operator. You will have to ensure that the arccosine values you
obtain in B lie in the appropriate angular range so that realistic values of g
and h are obtained.

Roger Stafford

"Roger Stafford"
<ellieandrogerxyzzy@mindspring.com.invalid> wrote in
message <g0i4o4$2lt$1@fred.mathworks.com>...
> "Nima Azar" <nimakev@yahoo.com> wrote in message
<g0i43e$n5i
> $1@fred.mathworks.com>...
> > Hi Guys,
> > So I'm measuring Reflectance(v2) vs. Wavelength(v1) and
> > need to find the thickness of my sample, for that I'm
> > trying to use fitting to a function using the nonlinear
> > square method to find couple of unknowns.
> > If anyone can help please email me at nimakev@yahoo.com
so
> > I'll send you more information,
> > any help is greatly appericiated.
> >
> > thank you.
> -------------
> I'm afraid my physics is a little rusty at this point.
You need to tell in what way
> sample thickness is to depend on reflectance and
wavelength in your fitting
> model.
>
> Roger Stafford
>
Try the following
write and save the following M-file
function f=v2(p,v1)
g=p(1);
h=p(2)
v2 = -a – b*v1 – c*(v1)^2 + d[1+(e/2d)cos((16.745*g/v1) +
h)] Exp(-j/(v1)^2)

on matlab main work space type
p=[1 1];
p=nlinfit(v1,v2,'f',p)
this should give you the best fitted parameters g=p(1) and
h=p(2)
please tell me how do you find thickness from reflectance I
need to know that
Aasim Azooz