Reflectance Spectroscopy - Science method

Great question... I wonder the same (looking the answer and didn´t find it) !

Hi,

Have you found a way to find these cross- and co-polarized components in Comsol?

You can record the spectrum of the reflected daylight and you will get some cues about the reflectance of the objects. But without standardized laboratory conditions with a specified light source you will not be able to calculate the reflectance. Daylight changes so quickly with atmospheric conditions, that it's impossible to use it a s a reference. Also your measurement in the dunes will include light that is not reflected from your object.

You will need to implement a kind of lock-in detection to remove the background. One possibility would be to use the same chopping also at the spectrometer side. If you acquire data with and without this additional chopping, a weighted difference should remove the background and provide the desired data.

The abovementioned method will work only if the light intensities are stable over the measurement time. A real lock-in detection, that does not have this drawback, would require another detector than the one installed in the spectrometer USB4000.

Dear Nilabja Kanti Sarkar,

I will take a stab at the question and hoe someone that knows a bit more will take over…

I am not particularly knowledgeable in PCAR but after reading these articles: https://arxiv.org/pdf/1210.6054.pdf and https://www.bnl.gov/isd/documents/93558.pdfI think it is similar to scanning tunneling spectroscopy (STS), as article number 2 uses a STM to conduct the measurements. In such case the STS probe the occupied and unoccupied local density of states (LDOS) or if a broader tip is used, I guess it is less local than STS of single atoms could be.

ARPES (see for example this review: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93.025006) probes the band structure of a material. If a UV lamp or other means of excitation is used it probes the occupied density of states. It is possible to probe unoccupied states using pump-probe laser setups or access parts of unoccupied states by doping.

The difference in this case would be that the STS measures the intensity of states for a range of binding energies whereas ARPES measures the reciprocal resolved intensity electron density for a set of binding energies. For one excitation energy you get k-parallel resolved band structure and if you vary energy you can get information about k perpendicular as well.

With ARPES you get occupied band structure (if using a standard setup not with laser or at a synchrotron) and with STS you get LDOS (also unoccupied states).

Best regards,

John

Metals are highly reflecting around 10.6 microns and transmittance should accordingly be close to zero already for a layer thickness of 50 nm, since the real part of the dielectric function of a metal is negative in this spectral range. So not much of the light should be absorbed, if the metal sheets are shiny.

Good day! Here I found brief and complex explanation on reflectance and transmittance phenomenons:

Thomas Mayerhöfer thank you very much!

Tushar Kumar Take a look:

1.

2.

3.

4.

Thank you so much.

You definitely want collimated light. A focused beam with its range of input angles hides features of the BRDF. For example suppose you have a mirror. A collimated input goes to a collimated output. These are essentially delta functions in angle space. However, if you put in a focused cone of light, you always at least get out that cone of light, a large range of angles in angle space regardless of the surface. Now say the mirror is slightly scattering. A collimated beam goes to a small diffuse cone. However the cone of focused light goes to a slightly fuzzier cone. The details of the BRDF of the surface are hidden in the large cone of the focused beam. In short, the angle measurement will be the convolution of the BRDF of the surface and the angular profile of the incident beam. If you want to measure the BRDF you want to convolve with as close to a delta function as possible.

larger the band gap, good will be the NLO activity

Hi Daniel,

the shape of the peaks in a specular reflectance spectrum depends on the oscillator strength. For peaks with comparably weak strengths, like those in organic and biologic matter, the absorption index function is also comparably weak, therefore reflection is dominantly influenced by the real refractive index function and the peaks have a derivative-like shape. For inorganic materials the oscillator strengths can be much higher and the same is true for the absorption index function, which increasingly influences the reflection spectrum until it dominates. Therefore the bands of oscillators with high strength are absorption index-like. If you want to learn more, check out my lecture notes:

Thank you for good discussion, is there any paper pointing out these information you mentioned V. N. Du Le ?

First of all it depends to the material studied, and for me i guess that IR is more better then UV cause its wavelength is bigger than UV.

By-election

Oh sorry Sir

For the sake of comparisons and the available standardised procedures, it is preferable to use absorbance under laboratory conditions. Except if you have customised equations for spectroscopic reflectance at difference wavelengths, then you can make comparisons between reflectance and absorbance.The traditional absorbance methods are robust enough to give you an idea of the amount of pigment in your samples. If you are doing method development, then, it will be interesting to see your findings.

Hi Armin,

I'm looking for the same properties of Ti-6Al-4V. Would you please let me know if you could find them?

Regards,

Eskandar

Thanks a lot.

HOPG is an unpolar substance, so it is not exactly great at absorbing infrared radiation which is why people usually characterize it by Raman spectroscopy. Here you can find extrapolated dielectric functions:

Even better, there are programs available with which you can analyze your spectra. E.g RefFIT by Alexey Kuzmenko (https://reffit.ch/) or CODE by Wolfgang Theiss (https://www.wtheiss.com/). Both have good manuals. Also SpIRIT by Konstantin Shportko (http://www.shportko.com/spirit.html) should be up to the task.

First of all, let me remark that UPS is a much better method for the investigation of valence band energies since the valence band has very low XPS cross sections and therefore you will end up with way too large error bars on your results.

If you have only XPS available, you proceed as follows:

Let us assume you have the usual setup: grounded sample, constant excitation energy, kinetic energy is measured with a CAE analyzer. Since you seem to be investigating a semiconductor I assume you are not troubled by charging effects.

Then your binding energy with respect to the Fermi energy is

E_B=E_rad-E_kin

In order to proceed, the ionization potential corresponds to the sum of the work function of your material and the binding energy of the first peak edge in your spectrum.

For more details, you can either refer to standard textbooks such as Ertl/Küppers or Hüfner (but the latter one is probably too deep for a starter) or check out manuals of analyzers. The Omicron manual is very good:

and for more details (especially baselines and peak fitting) the Casa XPS manual is actually more concise and helpful than any textbook I know:

After drying you most probably get a coffee ring effect, meaning that the thickness of you layers is strongly changing from point to point. Therefore imaging and measuring individual points might in any way not be the correct method for reasons explained in

The electric field standing wave effect can be corrected as explained in

My feeling is, however, that you should better use a different technique, maybe to coat an ATR crystal and see if you could obtain a calibration line, in particular also, because for near normal incidence and thin layers, you might see nothing at all on your metallic substrate due to the fact that a metallic surface suppresses electric fields parallel to its surface. Certainly, this still does not solve the problem of overlapping bands.

it seems unlikely that you mean solution. As mentioned above the metal oxides will be present in form of dispersion (note the difference solution - thermodynamically stable 1 phase system, dispersion 2 phase system, thermodynamically unstable).

As you can read in many discussions here on Researchgate - spectra will depend on size distribution of particles.

Little heavy in math, but the following article shows theoretical background of diffuse reflectance.

You can Google Kubelka-Munk theory and you will find tons of references you can use. The original Kubelka-Munk theory was published many years ago as follows.

Kubelka, P.; Munk, F. Ein Beitrag Zur Optik Der Farbanstriche. Zeitschrift für Technische Physik 1931, 12, 593-601.

Dear Afshan,

please compare the formula in your question and that in the reference . They are different. In the reference in the integral R(w) is substituted by R(w dash) such that one can one can get phi(w) at a given w while integrating over R(w).

Best wishes

for a new material how can find that its band gap is direct or indirect?

Hi Yazhou,

See attached, a part of my experimental data, corresponding to previous discussion.

You can invert, smooth, parametrize (or whatever) these experimental data.

Be careful that even if spectralon is a theorical reference, real material can be deteriorated getting used and aged. In other words, my spectralon is not exactly your spectralon.

This is the best I can do to answer.

Best regards.

亲切

Sorry to say that, but you compare apples and oranges. Absorbance does not refer to a particular measurement method. Correspondingly there exist transmittance absorbance (-lg T), reflectance absorbance (-lg(R/R₀) etc. relating to the method of measurement. Please be more specific in your question and let us know from which method of measurement the absorbance derives.

Can someone diffuse the mist surrounding this issue in my mind: how does one convert ToA reflectance to surface reflectance?

thank you sir

Thank you !

If they dont describe the exact amount of moisture content, then what information/ parameter do we get from NIR for hair fibres? is it possible to determine the same from any other technique ?

your point is not clear

Dear Christoph,

I am happy if it helped a bit.

Petr

Hello,

Here are a few additional papers (just follow the links) that you might find of use:

Best, John

The absorption of different constituents of human tissue has been extensively studied and many variations of the following graph can be found in literature and a quick google search.

Describing the interaction of light with skin is a complex challenge given the different interactions light has as a function of wavelength with different biological molecules. The low absorbance of NIR wavelengths as shown in the above link gives rise to the use of NIR in biomedical photonics. 

The following paper may be of interest if you haven't already seen it

Do you have a particular application in mind? For laser ablation you might want specific but high absorbance, whereas for imaging you will want low absorbance. 

 Dear Leila,

Maybe you misunderstood Vladimir's suggestion  to measure reflection from polished side of a Si wafer and to use it as reference. Use the formula you gave above with the same mirror to measure R of Si and compare your results with the literature data for Si. If you get right result for Si, then your simulation for nanostructure is wrong. If the result for Si is wrong, then check your experimental setup. Use metallic mirror. Deposited aluminium layer will be OK. Use a collimated beam with diaphragms to avoid different angles of incidence. Also you can use a beam splitter to achieve normal incidence. Measure reflection from the mirror and from the sample with the same slit width of the monochromator, only changing accumulation time (or amplification) if necessary  to avoid saturation of the detector. Then normalize signals from the sample, mirror and background to the same amplification (or accumulation time). Use your formula. Also, be concerned about polarizing effect of your momochromator grating if the incidence angle is not normal or if your nanostructure is birefringent.  Use a depolarizing  wedge.

It's ok since ther is incomplete light collection of light even by integrating sphere. You will get 100% after baseline recording. The reflectsnce of your samples will then calculated relative to your standard.

Dear Dr. Mahdi Karimi-Nazarabad

Assalamu alaikum 

Have a nice day and good times

Experimentally, You can get  the value of E^g by usually use the Tauc relation, which is given by this equation:                                

 αhν = A (hν - Eg )ⁿ

where α is absorption coefficient given by                

α = 1/t  ln [(1-R)² / T]

where t  is the sample thickness, T and R are the transmission and  reflection, while  (hν) is the photon energy, where:

hν(eV) = 1240 / [incident wavelength (nm)]

If you plot a graph between (αhν)^1/n  versus (hν), then you can get a straight line. This line intersects the X-axis at (αhν)^1/n = 0 . The values of E_g have been estimated from this intercept.  The value of n is dependent on the electronic transition type. Where:

n=1/2 for direct allowed transition,

 n= 2 for indirect allowed transition, 

n=3  for direct forbidden transition and

n=3/2 indirect forbidden transition. You should try to select the suitable n according to your samples and their preparations.

The appended papers may help you; they are examples of direct and indirect allowed transitions.

Good luck

Your,

Ahmed Saeed Hassanien

A couple of reflectance and transmittance spectra from the same sample can be found in the linked publication (calculations based on Fresnel's equations). There are definitely some differences...

Dear colleague Yeswanth Rayapati

Have a nice time and good day.

Herein fined all what you need about optical properties from A to Z. in details including the direct and indirect transition akso the references are included.

Due to the format of the Equations, it is included in the attached file so check the Eq. No. the see it in the attached file.

First you measure transmittance, T reflectance, R and/or absrobance using any spectrometer. 

If your spectrometer is not calibrated so you need to  calibrate your measured parameters otherwise go to step 2. Herein fined how to calculate the optical gap and constants of the film also the references are mentioned and all you need to overcame the all problems of optical properties [five items]. Due to the format of Equations it is attached in a separate file, just you know the equation number please check it through the attach file.

1- How to calculate the correction of T and R?

The reflectance was measured at normal incidence with an aluminum reference mirror. The absolute values of  transmittance, T and reflectance R of the substrates after correcting the  are given by [[**]A. A. Sagade,  R. Sharma, Sensors and Actuators B: Chemical, 133 (2008) 135-143 [**] M. Dongol, M. M. El-Nahass, A. El-Denglawey, A.F. Elhady, A.A. Abuelwafa. Current Applied. Physics 12 (2012) 1178.]

Equation No.……………………………...... (1)

Ift and Iq are the intensities of the light passing through the film-quartz system and the reference quartz, respectively, and Rq is the reflectance of quartz. In addition, if the intensity of light reflected from the sample mirror reaching the detector is Ifr and that reflected from the reflectance reference mirror is Im, then

Equation No.…………………… (2)

Ifr is the intensity of light reflected from the sample reaching the detector and Rm is the mirror reflectance.

T and R spectra were performed on thin film samples with single face. Extinction coefficient, k and refractive index, n were calculated using T, R and thickness d taking into account the experimental error of   the film thickness. T and R.

2- How to calculate  Absorption and extinction coefficient?

T, R and d are used to calculate the absorption coefficient, α

according to [[**]A. El-Denglawey, M. Dongol, M.M  El-Nahass, J. Lumin 130 (2010) 801.]:

Equation No.………………………….…….…… (3)

α is given by:

Equation No. …………………………………… (4)

The calculated α is included within high absorption region (α ≥ 104 (cm)-1).  

Extinction coefficient, k of TiO2 film is calculated by using:

 

Equation No. ……………………………………….…. (5)

3- How to calculate  Optical gap?

            An absorption edge of semiconductors corresponds to the threshold of charge transition between the highest nearly filled band and the lowest nearly empty band. According to inter-band absorption theory, the film’s optical gap can be calculated according to [[**]J. Tauc (Ed.). Amorphous and Liquid Semiconductors, Plenum, New York, 1976].

 

Equation No.…………………………. (6)

 A is a parameter of transition probability, it measures the disorder of material 

A = 4πσmin / nc∆E, Where  σmin is the minimum metallic conductivity, n is the refractive index, c is the light-velocity, and  ∆E = ∆Ec - ∆Ev   represents the  band tailing

[[**]M. M. El-Nahass, M. H. Ali, A. El-Denglawey Trans. Nonferrous Met. Soc.     China 22(2012) 3003−3011].  

is the optical gap of the material, hυ is the incident photon energy and r is the transition coefficient. The reported values of r are 2 for the measurement of indirect optical gap and 1/2 for direct optical band gap.

4- To determine the value of r plot the relation.

In case you know the value of Eg from the literature you can use:  ln (αhυ) = ln B+ r ln(hυ- Egopt) and find the value of r from the slope of the line for Ex.

 May you have both direct  and indirect band gap

The indirect optical gap, is evaluated by extrapolating the straight line part of (αhν)1/2 curves with energy axes (hυ) i.e (αhυ)1/2 = 0  according to eq:

Equation No.……………………………. (7)

Direct optical gap,  is evaluated by extrapolating the straight line part of (αhν)2 curves with energy axes (hυ) i.e (αhυ)2 = 0  according to eq:

Equation No.……………………………. (8)

Both direct, and indirect, optical gaps of TiO2 films may be found.

OR

to find the value of r the relation between (αhν)^1/r and incident energy (hν) for all values of r should be figured. The value of r which release a straight line represent the value of r and the electronic transition type.

5- How to calculate refractive index and dielectric constant?

Both R, and k at different λ were used to calculate refractive index, n according to:

[[**] T. S. Moss. Optical Process in semiconductor. Butter Worths, London, 1959.]

Equation No.     ………………………….… (9)

The dispersion of refractive index of the films is analyzed by the concept of the single oscillator and can be expressed by the Wemple–DiDomenico (WDD) relationship[ [**][S. H. Wemple, M. DiDomenico. Phys. Rev. B 3 (1971) 1338-1351] as: 

Equation No.          ……………….(10)

 Eo is the single-oscillator energy and Ed is the dispersion energy which is a measure of the intensity of the inter-band optical transition, it does not depend significantly on the band gap. The oscillator parameters can be determined  by fitting a straight line to the experimental points according to [[**][A. El-Denglawey. J. Non-Cryst. Solids 357 (2011) 1757-1763].

Plotting  vs (hν)2 allows to determine the oscillator parameters by fitting a straight line to the experimental points. By extrapolating the linear part of WDD optical dispersion relationship towards the infrared spectral region (hν = 0), static refractive index n(0), could be defined by the infinite wavelength dielectric constant ε∞ or n(0)2,

The relation between the lattice dielectric constant εL, and the refractive index, n as

[[**] A. El-Denglawey. J. Non-Cryst. Solids 357 (2011) 1757-1763.]:

Equation No. ………………………………….(11)

where εL is the lattice dielectric constant, N/m* is the ratio of the carrier concentration to the effective mass, c is the speed of light, and e is the electronic charge, εo is the permittivity of free space. The linearity of the plots of n2 versus λ2, verifying of Eq. (11). The value of εL is determined from the extrapolation of these plots to λ2 = 0 and N/m* from the slope of the graph.

Please notice that there is a direct calculation of ( hu) by this relation using wave length only.

E= hu =1240/wavelength (nm). 

I wish that is useful and help you.

Don't hesitate to ask about any thing concerning optical, electrical and structural properties.

Good luck

Yours

A. El-Denglawey

If you talk about the specular reflectance, a common reason is surface roughness... to give a more extensive answer, we would need more information about what kind of sample you measure in what spectral range by what method and instrument etc....

why we draw tangent? what is the reason behind this??

i think at (0,0) absorption is zero?

and one thing more why we take 1/2 and 2 for direct and indirect band gap?

For any LULC change detection study, the primary objective amongst others is to identify the changes which have occurred over a particular area. Therefore the object of interest is to identify the changes in land cover/land use and not the changes caused by atmospheric or radiometric effects or any other artifacts. As you know, when a satellite looks down on the earth, it also looks through a column of atmosphere which in a way obstructs the field of view of the satellite sensor before it senses the objects on the surface of the earth. Surface reflectance products as the name suggests are already corrected for radiometric and atmospheric effects. These pre-processing (radiometric and atmospheric corrections) steps which you anyway would have done with a normal Landsat product for carrying out a LULC change detection study, is now already been done for you when you use a Surface Reflectance product.

As these Landsat Surface Reflectance products are provisional, I would suggest you to manually carry out pre-processing steps and then compare your results with the Surface Reflectance products. Also go through the product guides for details.

As I understand correctly, you want to depict SMC. You need to have soil moisture for suction or metrics. You need a Pressure Plate to measure soil moistures at different pressures (negative pressure=suction). From Field capacity moisture (pressure=-0.33 atm to PWP((permanent wilting point)=-15 atm). You need at least 10 points to suitable distribution along this suction ranges.   

The best and most reliable way in my opinion is to measure the polarized IR-reflectance from a single crystal and to analyze these spectra by dispersion analysis employing suitable oscillator models. Thereby you not only get the dielectric tensor function, but also information concerning carrier density, oscillator positions etc.

Dear Aras, the curve is like that, it is just flat at a certain wavelength range, higher values could be detected.

Hi Amir,

there is no simple answer to you question since any wavelength interacts with tissue. So if you do not kwow which physical effect you want to study. Diffuse Reflectance is usually due to body scattering. Scattering itselfe is dependent on the wavelength and the size of the targets (and other things, maybe have a look at wikipedia or a textbook). 

You should also consider absoption. If you choose a wavelength that is, e.g. stongly absorbed by water it migth not give you much signal in refectance.

As for the difference between lasers and LED, laser are basically strictly monochromatic, means emitt light with one exact wavelength, LED emitt ligth with an band of wavelengths, means a maximum wavelength and bandwidth.

Hope that gives you some directions.

Not to be confused with REFLECTIVITY - not my area of expertise

Hi,

If you want to use the integrating sphere, you might not need to do sample prep with BaSo4.

I have worked a lot with integrating and double-integrating spheres in general, and this is how it works.

In integrating sphere, one places a thin layer of sample in a glass/quartz cuvette such that it covers the sample entry port of the integrating sphere completely. Integrating sphere offers the option of measuring DIFFUSE reflectance/transmittance. For diffuse reflectance measurement, you allow the light beam to enter from the port almost at 180 degree to the sample port, such that the collimated light travels in a straight line in the integrating sphere and then falls onto the sample. As one can imagine, a portion of light falling onto the sample will get reflected back through refraction within the sample. And this will be the DIFFUSE back scattered light. This will fall onto the walls of integrating sphere and will homogeneously diffused by multiple reflections within the integrating sphere. And you will find a detector port in the integrating sphere so that you can collect the diffuse light in the integrating sphere onto the detector.

It is worth to look at some work published by Prof. Scott Prahl (father/inventor of this tech). http://omlc.org/software/iad/

One good reference to start with: http://omlc.org/~prahl/pubs/pdfx/pickering93a.pdf

when you are adding some impurity into any material then it has its own energy states which you can call virtual states below or above the conduction band of host material

if the doping material has virtual states below the conduction band of host material then reduction in bandgap occurs

and vice versa.

Astro, but the problem here is that we have nothing to  do with the tauc plot, because there is reflectance data against the wavelength... so we can not have tauc plot for these values, how can we varify the bandgap (E_g) with having reflectance spectra...I heard there're some more methods for finding the bandgap as well... is it right? If yes what are they? Dr. Roberto

Diffuse reflectance accessories make the analysis of solid samples much easier instead of solutions (i.e. in UV-vis.) KMF is a very good tech to find the Energy band gap...

Here a file of Indium doped ZnO is attached that can help us understanding the DRS 

Thank you Riyad and Rajasheker. 

Hi Lukas!

Consider the following:

Reflectance is equal to the ratio of the reflected radiance and the incident radiance. The SPECIM radiance measurements correspond to the reflected radiance, while the FODIS measurements to the indicent radiance. Thus, to estimate the at-sensor reflectance you have to calculate the SPECIM/FODIS ratio for each one of the available spectral bands. Moreover, because the FODIS measurements are point data, the same FODIS measurement will be used for all the samples of each SPECIM line.

It is important that you pay attention to the following points:

Hope this will help,

Panagiotis

Hi,

Some research as: Assessing the spatial extent of breast tumor intrinsic opticalcontrast using ultrasound and diffuse optical spectroscopy Ang Li, Jing Liu, Wendy Tanamai, Richard Kwong, Albert E. Cerussi, and Bruce J.Tromberg, and other on the attached links reports the use of COMSOL trying to solve by FEM the model.

Please check the options and I hope you can find some tips.

Best wishes

Thank your for answer.

I want derivation of refractive index (n) 

Optical conductivity =  alpha x n x c/4pi

Hi,

regarding the reference measurement, there are two types of reference standards, specular reflectors like aluminum mirrors, and diffusive reflectors, for instance dielectric powders (BaSO4 is very common). It depends on your sample what is the right choice for you. In principle, it is desirable to have a standard whose reflection properties are similar to those from your sample. For instance, if you have a sample with a highly specular reflectance such as a thin metal film or a silicon wafer, a specular reflectance standard should be used.

Reference standards can be commercially purchased, but are quite expensive when they come along with a calibration certificate. A "low cost" solution is to use a sample with known optical constants as standard, for example a silicon wafer. The optical constants can be determined by an independent measurement such as spectroscopic ellipsometry. From the optical constants, the reflectance to be expected can be calculated using the Fresnel equations.

Hi Hristo,

I have some experience in using the Landsat surface reflectance product, and have eventually validated this product over the urban coastal environment of Hong Kong, you can have a look in the attached publication.

Regarding the conversion of the surface reflectance product into percentage you can consult the LEDAPS SR product guide.

Majid

Check for example the attached papers. There we studied in one case a film composed of several phases. Some information regarding them was extracted but layer thickness is not possible to calculate in cases like this using UV VIs as the refraction index would be the contribution of the each phase distribution in the film volume. In the other case we studied an copper oxide film over a metal substrate and we were able to subtract the contribution of each one and calculate thickness and n and k dispersion by the use of software SCOUT. For multilayer films I guess you could try SCOUT also (is not freeware) or software included in some apparatus to measure thickness (I remember that Ocean Optics have one), but a model of your system would still be needed to first guessing the optical parameters.

For band gap calculation, you require transmittance as well as reflectance along with the thickness of the films. You can use Tomlin's equations for determining extinction coefficient and then Tauc's plot will give you reasonable perfect value of band gap.   

It is ok but have you taken care to properly subtract the background and carry out the baseline correction to make it flat through zero?

Reflectance (and more generally UV-Vis, IR and Raman spectroscopy) are routinely used to monitor Spin Crossover with temperature/light/pressure, since HS and LS spectra are different enough that you can see the variation. Reflectance is a quick way to follow the variation with temperature since you can do it on powder, using homemade setups that avoid the constraints of cryostats needed for high-performance UV-Vis spectrometers.

At any temperature you will have a mixture of x complexes in HS state and 1-x in LS state. The spectrum of the sample will be the sum of both. Inversely you can extract x from the spectra provided you have a reference. Difficult to do with reflectance and more generally UV-Vis given the broadness of the bands, easy with IR and especially Raman if you find markers specific to one spin state.

Hi,

why not using gnuplot ? For example :

set parametric

set isosamples 30 , 30

Rx(u,v)=cos(u)*cos(v)

Ry(u,v)=sin(u)*cos(v)

Rz(u,v)=sin(v)

brdf(u,v)= .......

Brdfx(u,v)=brdf(u,v)*Rx(u,v)

Brdfy(u,v)=brdf(u,v)*Ry(u,v)

Brdfz(u,v)=brdf(u,v)*Rz(u,v)

splot [-pi:pi][0:pi/2] Brdfx(u,v),Brdfy(u,v),Brdfz(u,v)

Thank you very much Dr. Yarnold for your detailed answer and very interesting references as well. actually, I am asking about the method which maximizes the predictive accuracy and its package for R.

Best regards,

Said

If you're looking at diffuse reflectance, a typical conversion formula used is "Absorbance = Log(1/Reflectance). There are also some data processing software packages, e.g. Unscrambler X (Camo Software), which allow you to convert spectra between absorbance, transmission and reflectance units - though licenses can be a bit pricey

it is absorbance which the spectrometer records. Simultaneously it give transmittance spectra also which is related logarithmically to absorbance. In case of reflectance measurements there are only absorbance and reflectance values which we get. 

Actually the answer of "Can we calculate reflectance from transmission data?" is definitely "yes" in the case of transparent sample with smooth surfaces. For absorbing sample the answer also could be "yes". For example if the sample is thin film on known substrate someone can use transmittance data for determination of refractive index, extinction coefficient and thickness of the film and then using the already obtained data to calculate reflectance spectra by well known equations. I personally prefer matrix transfer formalism.