2 Science and Instrumentation Considerations for Infrared Solar Observations

There are several advantages which can be realized by observing the Sun at infrared wavelengths compared to observations at shorter wavelengths. These advantages concern the behavior of the Earth’s atmosphere and the telescope, as well as the physics of atoms and solar radiative transfer. While these factors play an important role in studies of the solar disk, they can be absolutely critical for studies of the faint solar corona. To be fair, there are also disadvantages to observing at infrared wavelengths, and these will also be discussed below. Borrowing from Harvey and Hall (1971*), presented below is a discussion of the advantages and disadvantages of making observations of the Sun at infrared wavelengths.

2.1 Instrument advantages in the infrared

2.1.1 Better atmospheric seeing

It has been known for a long time that seeing improves at longer wavelengths, and early work at infrared wavelengths suggested that atmospheric seeing was so minimal that many telescopes were seen to achieve their diffraction limit (Turon and Léna, 1970). Most modern ground-based solar observations do not settle for seeing limitations imposed by the atmosphere. New progress in the field of adaptive optics has resulted in superb image quality for images of the solar surface. Image stability is also key for spectroscopic and polarimetric studies of the Sun, especially when scanning the solar image is required to build a map of the solar surface.

Adaptive optics (AO) correction techniques have been discussed in many places and a good reference is the Living Reviews article by Rimmele and Marino (2011). The general aim of an AO system is to correct the effects of atmospheric turbulence on the wavefront measured by the telescope so that the total optical transfer function (OTF) of the telescope and the atmosphere approaches the OTF of the diffraction limit of the telescope. The wavefront distortions introduced by changing atmospheric refraction depend on the wavelength of the light observed. A quantity known as the Fried parameter r0 is used to characterize the atmospheric distortions integrated through the atmosphere. Early work from Karo and Schneiderman (1978) with stellar sources (and even earlier lab work) showed that the Fried parameter increase with wavelength as r0 ≈ λ6∕5.

This enters into the performance of an AO system in two ways. First the angular extent over which an image can be corrected by an AO system (also known as the isoplanatic patch) increases as r0 increases, and so at infrared wavelengths an AO system can correct a larger area of the solar image than at visible wavelengths.

The second advantage comes from a physical description of the Fried parameter; it represents a typical atmospheric size-scale with little distortion; a region of the atmosphere across which diffractive changes of the incident wavefront are minimal. The time-scale associated with the image distortions is given by the Fried parameter divided by the atmospheric wind speed (which moves the distortions across the telescope’s line of sight) TAO ≈ r0∕vatm. So for larger Fried parameter values, the time scale is larger, and the image changes more slowly. This means that AO system can work more slowly, and this is the second way in which AO correction is easier at longer wavelengths.

2.1.2 Less atmospheric scattering

Atmospheric scattered light has been studied for many years. The scattering at visible wavelengths in a clear sky was explained well by Lord Rayleigh (J. Strutt) as early as 1871 (Strutt, 1871) with single scattering from molecules in the atmosphere. Approximate solutions of electromagnetic scattering from particles smaller than the wavelength of light show a dependence on wavelength which varies as − 4 λ. Thus blue light is highly scattered, while red and infrared light is scattered less and transmitted more. Early infrared observations (Knestrick et al., 1962*) confirmed that while the amount of infrared scattering was much smaller than visible scattering, the wavelength dependence was flatter (see Figure 2*). At infrared wavelengths the particle size is closer to the wavelength of the radiation, and so the Rayleigh approximation does not work.

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Figure 2: Atmospheric scattered light as a function of wavelength from sea level measurements over water, taken in 1959 – 1960. Corrections for water vapor and methane absorption were made. The wavelength behavior of the scattering changes on different days, presumably depending on the particulates present during the testing. These particular measurements show at best a λ− 1.7 change, but at other times are nearly flat. Image reproduced with permission from Knestrick et al. (1962), copyright by OSA.

At infrared wavelengths, the Mie solution to the scattering problem must be used. Mie scattering solutions can be computed using a variety of scattering source sizes, and can represent different types of atmospheric particulates. Results of such calculations show only a small decrease with wavelength, and also show more complex wavelength behavior, determined by the molecules found in the scattering sources (Whittet et al., 1987).

2.1.3 Less instrumental scattering

Scattered light is present in all telescopes, reflecting and refracting. In the simplest model, a manufactured mirror will have small-scale deviations from the ideal shape. The root mean square of this deviation is known as the surface roughness, σ, and in the best case the surface roughness is small compared to the wavelength of light. Bennet and Porteus (1961) show that the diffuse reflection from such a surface will vary as (σ ∕λ)2, and Harvey et al. (2012) define the total integrated scatter (TIS) as the ratio of the diffuse reflectance to the specular reflectance, which also varies as TIS ≈ (σ∕λ )2. Harvey et al. (2012) also point out that it is important to use the relevent spatial scale of the surface roughness (generally the surface deviations on length scales of less than 1 mm) for these calculations. While deviations on larger spatial scales (sometimes known as figure errors) also contribute to scattering, and a more complete discussion of scattering is provided by calculating the bidirectional reflectance-distribution function (Nicodemus, 1970), the wavelength dependence of the BRDF is encapsulated in the TIS. So as observations move from visible to infrared wavelengths, the scattered light which disturbs those measurements decreases sharply.

For mirrors which are not perfectly clean, the situation becomes more complicated. As might be expected from the discussion of atmospheric scattering, the telescope scattering at infrared wavelengths is limited by scattering from dust contamination rather than from diffuse reflection caused by surface roughness. Surface contamination of the mirror by dust particles can be examined with Mie scattering solutions, but models of mirror BRDF at 10 600 nm reproduce the measured BRDF values only to a factor of 5 (Spyak and Wolfe, 1992a). So while moving from 1150 nm to 10 600 nm wavelength, the total scattering from an ideal mirror should decrease by a factor of 100, real measurements and also predictions from dust scattering models show that the actual scattering decreases by only a factor of about 20 (Spyak and Wolfe, 1992b). Scattering from dust on mirror surfaces is the dominant source at infrared wavelengths, and while the total scatter does decrease with wavelength, it decreases about a factor of 5 more slowly than surface roughness arguments alone would predict.

What scattered light has been observed at real solar telescopes? Staveland (1970) reports a wavelength dependence in the combined telescopic and atmospheric scatter, which drops faster than λ− 1 but not as steep as λ−4. Work at the McM-P telescope by Johnson (1972) provides total scattered light observations at the limb of the Sun from about 1000 nm to 20 000 nm. The data show a drop of only a factor of two from 1000 nm to 5000 nm, and then rather uniform scattered light at wavelengths towards 20 000 nm. This work also provides a numerical fit of TIS = 0.026 + 0.06(1 + λ∕1000 nm )e−λ∕1000nm, but this 40 year-old work should be re-examined with modern instrumentation.

2.1.4 Smaller instrumental polarization

A telescope introduces polarization to change the input polarization of light it recieves in ways which mix the different states, sometimes making it difficult to retrieve the original polarized signal. This process has been studies in great detail, and the parameter used to measure this change is the Mueller matrix. The Mueller matrix acts on the input polarization to produce the measured polarization state output by the telescope, which is given by: ⃗Sout = M ⃗Sin. Here ⃗S = [I,Q, U, V] represents the intensity of the four Stokes components of polarized light. In an ideal system the Mueller matrix is fully diagonal, and in the best case with no instrumental polarization it is equal to the identity matrix.

In a telescope with many optical elements, the total Mueller matrix can be constructed by multiplying the matrices from the individual elements. Balasubramaniam et al. (1985) specify the Mueller matrix for a reflection off of a single mirror as:

( 2 2 ) | 1 + X 1 − X 0 0 | || 1 − X2 1 + X2 0 0 || M = || 0 0 2X cos(τ) 2X sin(τ) || , (1 ) |( 0 0 − 2X sin(τ) 2X cos(τ) |)
where the terms X and tan(τ) are dependent upon the angle of incidence, and the real (n) and imaginary (k) components of the index of refraction. For values of X approaching 1.0 and τ approaching zero, the Mueller matrix becomes diagonal and instrumental polarization effects are reduced. This occurs for increasing values of either n or k.

Aluminum is often used as a mirror surface, and the index of refraction of aluminum has been measured through a large wavelength range. In the infrared spectrum, the value of k increases, and for values of wavelength greater than about 1250 nm, the value of n also increases (Rakić, 1995). An aluminum mirror introduces less instrumental polarization through the infrared spectrum.

While many infrared telescopes and instruments use all-reflecting optical systems, some telescopes also use transmissive optics in the infrared. Additionally, as metal coatings on mirrors are exposed to the air, metal oxide layers build up which also act as transmission elements in the optical system. With these added complications, do real telescopes also show a decreasing instrumental polarization at infrared wavelengths? Socas-Navarro et al. (2011*) made measurements of the Mueller matrix of the NSO/DST (which includes transmissive optics) as a function of wavelength from 470 nm to 1413 nm. The infrared coverage is not large, but clear trends can be seen from 1000 to 1413 nm in their analysis. All the off-diagonal terms in the matrix decrease in value and in some cases are already very close to zero at 1413 nm (see Figure 3*). At the all-reflecting NSO/McM-P facility, studies at 12 000 nm show that the off-diagonal terms in the telescope matrix were expected to be at the level of about 1% or less, (Deming et al., 1991a) and measured to have an upper limit of 4% (Hewagama, 1991).

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Figure 3: A schematic representation of the wavelength variation of the Mueller matrix of the DST. In each box the wavelength dependence of the value of the matrix element is plotted from 400 – 1600 nm. What is important to note is that the off-diagonal elements, which represent the polarization cross-talk, approach a value of 0 as the wavelength increases. Image reproduced with permission from Socas-Navarro et al. (2011), copyright by ESO.

2.2 Instrument disadvantages in the infrared

2.2.1 Larger diffraction limit

At longer wavelengths, a given telescope will have less spatial resolution. The diffraction limit of a telescope represents the ability to resolve small objects, or to distinguish two closely space objects. The diffraction limit is often defined as the distance between the central peak and the first minimum of the Airy pattern resulting from diffraction by a telescope’s primary aperture. With a diameter of D the angular separation in radians is given by 𝜃 = 1.22λ∕D but this is often simplified as just 𝜃 = λ∕D. To compute the diffraction limit in arcseconds when λ is in units of nm and D is in units of mm, we find 𝜃 ≈ 0.2λ ∕D.

2.2.2 Increased background levels

According to Wien’s displacement law, a black body with a temperature of 300 K will have its continuum emission peak at a wavelength of 9656 nm, but at wavelengths shorter than that value, such a body will emit a large amount of radiation. Starting at wavelengths of about 3000 nm, room temperature telescopes and feed optics glow and this emission provides a background value against which a target object must be measured. This increasing background level is the other key disadvantage of observing the Sun at infrared wavelengths.

Cryogenic cooling is used to minimize this thermal background. Infrared arrays are cooled to much lower temperatures than visible cameras are cooled. Often several feed optics upstream of the infrared array are cooled, and of particular importance is the cooling of a narrowband filter. Interference filters or, in some cases, diffraction gratings are used to limit the spectral range of flux incident on the infrared array in order to avoid thermal contamination. To be effective, these filters must themselves be cooled to cryogenic temperatures, usually at or below the temperature of liquid nitrogen (77 K). Such cooling efforts then required evacuated dewars to house the cold detectors and optics.

Even with excellent cooling, some infrared observations are still subject to high levels of background contamination. Such observations fall into the realm of background-limited observations, in a similar way that ground-based observations of the solar corona at infrared and even shorter wavelengths are background-limited (Penn et al., 2004b). In an effort to accurately measure the large background and subtract it, a variety observational methods have been developed, including chopping between on-target and off-target.

2.2.3 Atmospheric and transmissive optics absorption

Absorption bands from the Earth’s atmosphere in the solar spectrum are not limited to infrared wavelengths; there are several in the visible spectrum, and the ultraviolet and some radio and sub-mm wavelengths are also impacted. Larger swaths of the infrared solar spectrum are not visible from the surface of the Earth, and so this is a disadvantage when compared to the visible spectrum.

Finally, some well-known optical materials do not transmit some infrared wavelengths. For example, telescopes with transmissive optical elements made from the commonly used BK7 crown glass have an wavelength cutoff at about 2500 nm; fused silica lenses have a wavelength cutoff at about 2300 nm. This issue is no longer a large difficulty, as transmissive lenses made from CaF2 or MgF2 are readily available and transmit up to about 6000 nm, and other optical materials are available for wavelengths longer than this.

2.3 Scientific advantages in the infrared

2.3.1 Increased Zeeman resolution

The wavelength splitting of atomic sublevels in the presence of a magnetic field increases as 2 geffλ increases, where geff is the effective Landé g-factor for the electron transitions forming a particular spectral line. The Landé g-factor is usually calculated with atomic models that couple total orbital angular momentum and total spin angular momentum first (known as Russell–Saunders or LS coupling) and the work of Beckers (1969) provides values of geff for many lines. While many lines have values of geff between 1.0 and 3.0, there are spectral lines seen from the Sun which can have larger values (Harvey, 1973a).

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Figure 4: The benefit of making magnetic field Zeeman observations in the infrared is shown in this figure. On the left is a plot showing the separation of the Stokes V peaks for various Voigt profiles at a magnetic field of 1 kG for a visible line and an IR line. On the right is a plot showing the value of the Stokes V amplitude. The Zeeman splitting of the 1565 nm IR line is fully resolved at this magnetic field strength, and the weak field approximation does not need to be used to interpret the spectra. Image reproduced with permission from Stenflo et al. (1987*), copyright by ESO.

The Doppler broadening of spectral lines due to macro and micro-turbulent velocities on the Sun increases linearly as λ increases. Magnetic field measurements measure a shift in the components of a spectral line, and this shift is most easily measured if it is large relative to the observed line width (see Figure 4*). So the ratio of the Zeeman splitting divided by the spectral line width gives us a measure of the magnetic resolution of a spectral line, and that value is geffλ. In order to make observations with the highest possible magnetic sensitivity, lines with large values of geffλ are sought in the solar spectrum, and while some spectral lines can be found with increasing values of geff (for example, selecting a different line may change the magnetic sensitivity by a factor of 4) it is usually more advantageous to increase the wavelength of the observations (changing from 500 nm to 5000 nm can increase the magnetic sensitivity by a factor of 10). Ideally spectral lines with inherently large geff and with long wavelengths are the best for making sensitive magnetic measurements.

Table 2 lists the magnetic sensitivies of some spectral lines with their respective magnetic sensitivies.

Table 2: Magnetic Sensitivity of Spectral Lines
Region Atom Wavelength [nm] geff λgeff
Photosphere Fe i 525 3.0 1575
Fe i 630 2.5 1575
Fe i 1565 3.0 4695
Ti i 2231 2.5 5778
Fe i 4064 1.25 5080
Fe i 4137 2.81? 11625 ?
Mg i 12318 1.0 12318
Chromosphere Ca i 854 1.1 939
Mg i 3682 1.17 4307
Ca i 3697 1.1 4067
Corona [Fe xiv] 530 1.33 706
[Fe xiii] 1075 1.5 1612
[Si x] 3934 1.5 5901

2.3.2 Large number of molecular rotation-vibration lines

Due to the structure of the several common molecules, the energy difference between rotation-vibration states of the molecule produces spectral lines which are found at infrared wavelengths. While the energies involved in these transitions are only completely described by a quantum mechanical treatment of the molecule, a simple classical physics analysis gives some insight about why this occurs. Setting the molecular rotational energy equal to the thermal energy of the solar plasma gives us 2 2 Iω ≈ (mr )ω char ≈ kT. Using T = 6000 K and order of magnitude masses for an oxygen atom and distances found in a water molecule, we can compute the rotational frequency to be ω ≈ 104 GHz. This corresponds to a wavelength of about 25 microns, and this is one way to consider why the solar IR spectrum contains many molecular transitions. On the Sun molecules exist in only the coolest regions but are destroyed by dissociation in all other regions. In this way, molecular spectral lines provide unique ways to probe cool regions around sunspots and near the temperature minimum region of the quiet solar atmosphere. Also of note is that molecular transitions have a range of Zeeman sensitivities and, thus, provide a unique probe into the solar magnetic fields in this cool plasma. Molecular spectral lines also provide a convenient way to measure atomic isotopes, as the subtle nuclear mass changes can result in larger wavelength shifts for molecular lines than atomic lines.

2.3.3 Ability to probe different heights in the solar atmopshere using continuum radiation

From 1000 to 10 000 nm, the height of formation of the solar continuum emission varies from roughly z = –40 km to z = 140 km. While the dominant form of continuum opacity at visible wavelengths is caused by H-minus bound-free transitions, at infrared wavelengths longer than about 1600 nm the dominant process changes to H-minus free-free opacity. The transition between the two processes allows photons to escape most easily from the solar plasma, and because of this we can view the deepest layers of the solar photosphere with observations of the continuum at 1600 nm. According to the VAL models (Vernazza et al., 1976*) photons at 1600 nm originate from about 40 km below the level at which photons at 500 nm escape. While this may seem like a small height difference, due to the photosphere’s which large density gradient there are changes in the solar magnetic fields which can be seen across this height change. Thus, spectral lines in the IR probe deeper regions where the magnetic fields are stronger than the regions measured by spectral lines at visible wavelengths. Over the range of heights probed by the infrared continuum, the solar convective granulation undergoes a radical change, reversing the intensity contrast completely. At the lowest layers probed by the infrared continuum, the center of granules are bright and the intergranular lanes are dark, whereas in the upper layers the reverse is true (Leenaarts and Wedemeyer-Böhm, 2005*; Cheung et al., 2007*). The height change of the infrared continuum thus provides a critical probe of the vertical structure of solar granulation.

At wavelengths longward of 1600 nm, the H-minus free-free continuum opacity increases and photons which we observe originate at higher levels in the solar atmosphere. At wavelengths near 1600 nm the τ = 1 level moves up through the solar atmosphere about 25 m per nm of wavelength, but at wavelengths near 10 000 nm the change decreases to about 15 m per nm. We can generate approximate fits predicted by various models using the log10 of the reciprocal of the wavelength. The approximate height of the τ = 1 level (in units of km) according to the VAL model is z = − 776 − 227 log10(1∕ λ) (see Figure 5*), and from another calculation by Gezari et al. (1999*) z = − 1049 − 303 log10(1∕ λ), where λ is in units of nm. Each of these approximations is valid only at wavelengths between about 2000 nm to 20 000 nm.

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Figure 5: The height of formation of the infrared continuum radiation is shown in this figure. The continuum radiation is formed at the deepest level in the Sun at 1600 nm, and then the continuum formation height increases with increasing wavelength in the infrared spectrum. The bottom plot shows that the dominant source of opacity is from Hydrogen free-free transitions. See also Fontenla et al. (2006) for more recent work. Image reproduced with permission from Vernazza et al. (1976), copyright by AAS.

2.4 Scientific disadvantages in the infrared

2.4.1 Fewer solar photons

The solar spectral intensity closely follows a black-body curve with an effective temperature between about 5800 K and 4300 K (Boreiko and Clark, 1987) although this varies with spatial position on the solar surface. At this temperature the peak of the black-body curve is in the visible spectrum and so the Sun radiates fewer photons in the infrared spectrum than it does at visible wavelengths. For wavelengths much longer than the peak of the black-body spectrum, the Rayleigh–Jeans law can be used to express the number of photons per second, per unit surface area, per solid angle, and per wavelength bin emitted by a black-body. The wavelength form for this Law is 4 B λ(T ) = 2ckT∕ λ. In order to maintain a constant spectral resolving power given by R = λ∕Δ λ, one must increase the wavelength bin size Δ λ as λ increases, to achieve the same velocity and Doppler broadening sensitivity. But even with the ability to bin in wavelength more, the number of IR photons available to observe the Sun at the same effective Doppler resolution changes as λ−3. Since the signal to noise of a particular measurement varies as the square-root of the number of photons which are measured, the signal to noise of a given spectrum decreases due to fewer solar photons as −3∕2 λ at infrared wavelengths compared to visible wavelengths.

2.4.2 Fewer atomic absorptions

The energy range of photons for the infrared spectrum as we defined in Section 1, spans about 1 eV to 10–3 eV. In order to form absorption lines at these low photon energies, the energy difference between the atomic levels must be small. Such small energy differences are usually found in upper levels (with large total quantum number n) of most atoms. The level populations of these high n states are usually quite low in solar plasma, so there are few opportunities for atoms to absorb infrared light. The infrared solar spectrum contains fewer atomic absorption lines than shorter wavelength regimes, and they are usually weaker. Some exceptions exist, such as spectral lines formed by electrons cascading through these upper levels after recombination of electrons, but, in general, atomic absorption lines decrease in their predominance as the wavelength increases. One advantage of this is that with fewer lines the infrared spectrum contains cleaner line profiles, free from the blending seen at shorter wavelengths.

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