# Reflectance Spectroscopy & Colorimetry

Abstract: in this post we describe the application of the Thunder Optics SMA Spectrometer and the Spectragryph software in reflectance measurements. We will apply the reflectance spectroscopy technique to the study of some materials.

### Introduction

In the previous post: Thunder Optics Spectrometer & Spectragryph, we described the Thunder Optics SMA Spectrometer (hereafter referred to as the TO spectrometer) and used it to acquire the spectra of some light sources. We now continue the experimentation activity by “exploring” with this equipment, with its accessories and with the spectragryph software, the technique of reflectance spectroscopy. In particular we will use this technique to analyze the light reflection of a set of materials of particular interest.

### The Measurement of Reflectance

Subjected to light radiation, each body has certain properties of reflection, absorption and transmission of light. The reflectance (ρ) represents the reflecting power of a body subjected to irradiation. It is a dimensionless percentage parameter. The sum of the parameters of reflectance (ρ), transmittance (τ) and absorbance (α) always gives 1, that is: α + ρ + τ = 1, easily demonstrable relationship considering the law of conservation of energy: a part of the incident energy is reflected, a part is transmitted, a part is absorbed. The reflectance value can be calculated using the following formula:

ρ = Φr / Φ0

Where Φ0 e Φr are respectively the incident light intensity and the reflected intensity from the sample under examination.
There are two models that can be used to calculate reflected light intensity: the perfectly diffusing, or Lambertian, reflection model, and the perfectly specular reflection model. These represent the two limit cases and therefore can approximate well the behavior of only few objects, while for most of the real cases the reflection can be considered a middle way between the two limit cases. The perfectly diffused reflection model predicts that light, after hitting the surface, spreads in all directions of space. The surface can therefore be considered as a spherical secondary light source. This behavior is typical of rough and opaque materials. The perfectly specular reflection model, on the other hand, foresees that the light beam hits the surface of a body and is reflected symmetrically with respect to the normal to the surface. With this model, the behavior of mirrors, for example the shiny surfaces of metals, can be well approximated.

In general, the reflectance value for a particular object essentially depends on the color and characteristics of its surface: very dark surfaces tend to values ​​close to 0 while light surfaces can have values ​​between 0.7 and 0.85.

Spectragryph software automates the calculation of absorbance. The selected measurement mode defines the type of y-axis of the measured live spectrum: intensity, transmittance, reflectance, absorbance (Fig. 1). We will choose the reflectance mode.

Fig. 1 – Measurement Mode Selection

Depending on the chosen modality, one or more auxiliary spectra may be required. The auxiliary spectra are the Dark spectrum, the Reference spectrum and the Blank spectrum. Each of these can be set, removed and viewed at any time. As soon as they are registered, they are stored and kept ready for later use. To update them, simply set them up again with a newly measured live spectrum. The Dark spectrum (Fig. 2) and Blank spectrum (Fig. 4) are optional, so their use must be activated by clicking on the respective button. The Reference spectrum (Fig. 3) is always mandatory except for the intensity mode, when necessary it is used automatically by the system.

Fig. 2 – Dark spectrum assignment

Fig. 3 – Reference spectrum assignment

Fig. 4 – Blank spectrum assignment

Measurement mode of auxiliary spectra:

• Dark spectrum: light source off, shutter closed, no light reaches the detector, mode: intensity
• Reference spectrum: light source on, full light (100% level) reaching the detector, modeintensity
• Blank spectrum: with “blank” sample (eg pure solvent or buffer in the sample container), with the final measurement mode selected

Each spectrum should be re-measured after changing the exposure time, furthermore the reference spectrum should be updated after any change in intensity of the excitation light.

The reference light source should have a spectrum as flat as possible over the entire range of wavelengths of interest. Lamps of this type are for example halogen or xenon lamps. If such a lamp is not available, a different light source can also be used, as long as it has a constant intensity over time. We used Thunder Optics Mini Light Source.

To improve the accuracy of the measurement it is always recommended to acquire the dark spectrum and activate its use, the same applies to the blank spectrum. Generally for each measurement context it is necessary to evaluate which auxiliary spectra has to be acquired and used. In general, the formula used by the software for calculating the reflectance is the following:

Reflectance: Live = (Raw – Dark) / (Reference – Dark) – Blank

In general, the reflection spectrum of a white Teflon tape (Fig. 5) is adopted as the reference spectrum, which therefore produces a reflectance spectrum equal to 100% (Fig. 6).

Fig. 5 – Teflon reflectance spectrum (reference)

Fig. 6 – Reference spectrum expressed as reflectance

### Materials and Methods

A Y optical fiber probe is used to measure the reflectance of the materials (Fig. 7). In practice it is a “bifurcated” optical fiber; two ends are connected to the light source and to the spectrometer, while the third end constitutes the actual probe which must be placed near the surface to be analyzed. The two optical fibers terminate at the probe: one carries the light emitted by the source while the other collects the reflected light and carries it to the spectrometer.

Fig. 7 – Y-Probe

In Fig. 8 we show the experimental setup which includes the SMA Thunder Optics spectrometer, the Mini Light Source and the Y-shaped optical fiber. The fiber head is fixed to a support stand so that the distance between the probe and the the surface to be analyzed can be trimmed.

Fig. 8 – Setup for reflectance measurements

In Fig. 9 we show the detail of the probe during the analysis of the surface of a white Teflon tape (to obtain a reference spectrum) and during the measurement of the surface of a colored card.

Fig. 9 – (a) Detail of reflection probe on teflon tape (b) Detail of reflection probe on red cardboard

### Colorimetry

The first reflectance measurements were made on simple colored paper to evaluate the different reflectance spectrum as a function of color (Fig. 10). This is the starting point for colorimetry measurements, which we did not do quantitatively but simply qualitatively. As can be seen from Fig. 10, the reflectance spectrum makes it possible to easily distinguish the different color of the paper surface. It is noted that for all the paper samples examined the reflectance in the near infrared range is high.

Fig. 10 – Reflectance spectra of colored cards

The same reflectance measurements were made with a series of colored pencils (Fig. 11), obtaining the spectra shown in Fig. 12. The graphs clearly show the correspondence between the surface color and the reflectance spectrum.

Fig. 11 – Colored pencils

Fig. 12 – Reflectance spectra of colored pencils

### Reflectance Measurements of Various Materials

In addition to the color of the surface, the reflectance measurements provide information related to the type of material and the physical characteristics of the surface. In Fig. 13 we report the reflectance spectrum of a black anodized aluminum surface. The black color results in low reflectivity at all visible wavelengths. In the near infrared, above 700 nm, the reflectivity however increases considerably up to values ​​close to 100%: our aluminum sample is black in the visible but not in the infrared range!

Fig. 13 – Black anodized aluminum reflectance spectrum

As known, metals have high reflectivity thanks to the free electrons in their crystal lattice. If the surface is adequately treated, they show specular and non-diffusive reflection and therefore they are not suitable for reflectance spectroscopy. We circumvented this limitation by examining samples consisting of metal powders: iron, aluminum and copper, together with a (non-metallic) sample of copper sulfate (Fig. 14). The spectra of metal powders are shown in Fig. 15 while the copper sulfate in Fig. 16. The reflectances of the dust samples are, as expected, rather low, aluminum and copper have higher values ​​than iron, while the copper sulfate (of a beautiful blue color) shows a maximum of reflectivity on the 450 nm – 500 nm.

Fig. 14 – Samples of powdered metals and salts

Fig. 15 – Metals reflectance spectra

Fig. 16 – Copper sulfate reflectance spectrum

The other materials we have examined are two leaves (Fig. 17-a), one green and therefore rich in chlorophyll, and the other dry, with a lower content of chlorophyll and a higher content of other pigments such as carotenoids and anthocyanins. We also examined the reflectance of a silicon single crystal and a graphite sample (Fig. 17-b).

Fig. 17 – (a) Green leaf and dry leaf (b) Graphite and silicon

The reflectance spectra of graphite and silicon are shown in Fig. 18, the silicon crystal has low values, while the graphite sheet has a surprisingly high reflectivity value, probably due to the high degree of surface finish.

Fig. 18 – Reflectance spectra of silicon and graphite

The reflectance spectra of the leaves are shown in Fig. 19, where the difference between the spectrum of the green leaf and the spectrum of the dry leaf is evident. The green leaf has a minimum of reflectance at the red wavelengths while the dry leaf has high reflectance also at the yellow and red wavelengths.

Fig. 19 – Reflectance spectra of green and dry leaves

### Conclusions

Our apparatus consisting of Thunder Optics SMA Spectrometer, mini light source and optical fiber Y-probe proved to be more than adequate for the qualitative analysis of the reflectance of the materials we examined. Analyzes of this type generally make use of halogen or xenon light sources, which guarantee an intense emission with a “flat” spectrum compared to an incandescent lamp. The spectrometer and the spectragryph software have however adequately compensated the non-constant spectrum of the light source used, allowing to obtain excellent results.

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