Análisis correlacional de las variables de estudio

Spectrometer stray light is light detected at a certain wavelength range of the measured spectrum, although it is not directly projected onto the detector. It can originate e.g. from grating diffraction maxima of higher orders or from reflections due to imperfect matching of the optical components within the Czerny-Turner set-up of the spectrograph. The intensity I_meas measured at the detector can be expressed as the sum of the signal I and the stray light IS:

I_meas(λ) = I(λ) + I_S(λ). (7.2)

In order to assess the impact of stray light on the optical density, Equation 7.2 is inserted into Equation 4.8:

−τ (λ) = ln I_meas(λ) I₀⁰(λ)



= ln I(λ) + I_S(λ) I₀⁰(λ) + I_S(λ)



. (7.3)

According to Platt and Stutz (2008), it can be assumed that the stray light contribution is small as compared to I(λ) and I₀⁰(λ) and that ln(1 + x) ≈ x, i.e. the Taylor expansion is stopped after the

term of first order. Equation 7.3 can thus be rewritten in the following way:

Hence, stray light reduces the optical density of Fraunhofer lines by the ratio ^I_I^S0^(λ)

0(λ) (Platt and Stutz, 2008). As a first stray light test the Fraunhofer lines of measured scattered skylight spectra in the UV and visible wavelength are compared to a high-resolution solar reference spectrum that is convolved to the resolution of the instrument.

In order to quantify the spectrometer stray light, spectra of a halogen lamp and of scattered sunlight are recorded with and without different optical filters. Figure 7.10 shows the internal transmittance of the different filters that are used for these measurements. In the following, for the QE, a GG420 filter is used, which cuts off light between 200 and 400 nm and has a throughput close to 1 at wavelengths above approximately 500 nm. For the USB a UG11 filter is used, which prevents light between 400 and 650 nm from reaching the detector.

Figure 7.10: Internal transmittance of the SCHOTT filters used for the stray light measurements, adapted from http://www.schott.com/advanced_optics/german/download/index.html).

After offset and dark current, the ratio of stray light and light can be calculated according to the following equation:

S = straylight

light = I_S

I_meas− I_S = I_filter

I_nofilter− I_filter. (7.9)

7.2. Instrumental characterisation 81

Figure 7.11a shows the results of the stray light measurements using a halogen lamp, whereas Figure 7.11b presents the results using scattered skylight as a light source. The halogen lamp spectra of the QE show a large fraction of stray light, which increases towards higher wavelengths where the overall intensity of the QE is reduced due to an unknown reason (Section 7.1). Although the GG420 filter completely blocks the light in the wavelength range of the QE, a stray light socket of approximately 40 to 80 % is left. As the halogen lamp has its maximum intensity in the near-infrared region, the stray light test is also performed with solar scattered light where the contribution of stray light from the near-infrared region is smaller due to the solar spectrum with T = 5800 K. Except for the wavelength range between 380 and 400 nm, the solar stray light reaching the QE results in values between 5 and 10 %. This number is quite large in comparison to the specifications of the manufacturer (0.4 % at 435 nm (http://www.oceanoptics.com/technical/QE65000.pdf)), but comparable to other spectrometers as e.g. the OMT spectrometers (H¨uneke, 2011).

In comparison to the QE, the USB shows very little stray light, both for the halogen lamp spectra (Figure 7.11a) and the scattered skylight spectra (Figure 7.11b). The mean value for S amounts to less than 0.1 %, which is in line with the specifications of the manufacturer (< 0.1

% at 435 nm (http://www.oceanoptics.com/technical/engineering/USB2000%20OEM%20Data%

20Sheet.pdf)). Obviously, the USB already has a built-in stray light trap.

A possible reason for the large stray light amount of the QE might be the wrong f-number. If the f-number of the fibre bundle or lens exceeds the f-number of the spectrograph, the incoming light overfills the collimating mirror, which can then lead to reflections at the interior walls of the spectrograph. Both fibre bundles have a numerical aperture of NA = 0.22, respectively. This results in an f-number of:

f /# = 1

2 · N A ≈ f /2.27. (7.10)

The telescopes of the mini-DOAS instrument further include quartz lenses with a focal length f of 30 mm and a diameter d of 12.7 mm, respectively. This leads to an f-number of:

f /# = f

d ≈ f /2.36. (7.11)

The f-number of the lens should match to the f-number of the spectrographs, which corresponds to f/4, both for the QE and USB. The f-number of the spectrographs is approximately 40 % larger than the f-number of the lens. Hence, the detector is overexposed leading to additional stray light.

Unfortunately, this feature was not considered in the original set-up by Simmes (2007). For further deployments, it is recommended to include a special cover plate in front of the quartz lens to avoid overexposure. Furthermore, an optical bandpass filter should be implemented, e.g. the U-340 filter (http://www.hoyaoptics.com/pdf/U340.pdf), which completely removes light coming from the infrared wavelength region.

Stray light can be accounted for in the DOAS fitting procedure by including an additional stray light polynomial (Section 8.3.1). Hence, it is assumed, that the effect of stray light is corrected during the DOAS fitting procedure and the accuracy of the results of the DOAS evaluation are not strongly affected by the stray light.

(a)

(b)

Figure 7.11: Stray light measurements using (a) a halogen lamp and (b) scattered skylight for the QE (upper panels) and the USB (lower panels), respectively. The left panels show the intensities without filter (I_nofilter, red line) and including a filter (I_filter, black line). The right panels show the ratio S according to Equation 7.3.

7.2. Instrumental characterisation 83