The COSMO coronagraph optical design and stray analysis Dennis Gallagher*a, Zhen Wub, Brandon Larsona, Peter G. Nelsonc, Phil Oakleya, Scott Sewella Steven Tomczyka aThe National Center for Atmospheric Research High Altitude Observatory-Boulder, Colorado, bNanjing Institute of Astronomical and Technology- Nanjing, China, cSierra Scientific Solutions- Boulder, Colorado

ABSTRACT

The Coronal Solar Magnetism Observatory Large Coronagraph (COSMO-LC) is a 1.5 meter Lyot coronagraph dedicated to measuring magnetic fields and plasma properties in the solar corona. The COSMO-LC will be able to observe coronal emissions lines from 530-1100 nm using a filtergraph instrument. COSMO-LC will have a 1 degree field of view to ob- serve the full solar corona out to 1 solar radius beyond the limb of the . This presented challenges due to the large Etendue of the system. The COSMO-LC spatial resolution is 2 arc-seconds per pixel (4k X 4k). The most critical part of the coronagraph is the objective that is exposed to direct sunlight that is five orders of magnitude brighter than the corona. Therefore, it is key to the operation of a coronagraph that the objective lens (O1) scatter as little light as possible, on order a few parts per million. The selection of the material and the polish applied to the O1 are critical in reducing scattered light. In this paper we discuss the design of the COSMO-LC and the detailed design of the O1 and other key parts of the COSMO-LC that keep stray light to a minimum. The result is an instrument with stray light below 5 mil- lionths the brightness of the sun 50 arc-seconds from the sun. The COSMO-LC has just had a Preliminary Design Re- view (PDR) and the PDR design is presented.

Keywords: sun, coronagraph, corona, scatter, dust, lens

1. INTRODUCTION

The Coronal Solar Magnetism Observatory Large Coronagraph (COSMO-LC) is a 1.5 meter aperture coronagraph that will observe the solar corona from 1.05 out to 2.0 solar radii. The wavelength span for COSMO-LC is (530-1100 nm) which includes key coronal emission lines such as Fe XIV 530.3nm, Fe X 637.4nm and near IR lines such as Fe XIII 1074.7nm, and the He I 1083.0nm chromospheric line. The High Altitude Observatory (HAO), a division of the National Center for Atmospheric Research in Boulder, CO currently operates two 20cm coronagraphs, the white light COSMO-K Coronagraph [1] and the Coronal Multi-channel Polarimeter (CoMP) instrument [2] on Mauna Loa on the big island of Hawaii. These coronagraphs observe the solar corona from 1.05 solar radii out to 3.0 solar radii. A very preliminary de- sign of the COSMO-LC was presented in 2012 [3]. HAO has performed several design trades and studies on various aspects of the COSMO-LC. The work presented in this paper is an extension of one of these studies that explores COS- MO-LC and stray light [4-5]. A key design requirement for a coronagraph is to reduce stray light in the instrument. The sky brightness next to the sun, ~1 arc-minute from the solar limb, on a clear day at locations such as Mauna Loa, located at an altitude of 11300ft, can be as low as a few millionths the brightness of the solar disk. Coronal emission lines are highly variable in brightness, but are typically in the range of 5-100 millionths of the brightness of the solar disk at ~ 1 arcminute from the solar limb. Therefore it is important that the design of a coronagraph have instrumental scatter as low as a few parts per million if observations of the corona are to be made with good signal to noise. Practically all the in- strumental stray light in a coronagraph is due to scattered and diffracted light from the O1 objective lens. The bulk of the scattered light is due to small polishing defects, mirco-roughness, and dust on the surface of the objective that are ex- posed to the direct sunlight. Diffracted light is controlled though the design of the Lyot coronagraph. In a coronagraph, an occulter blocks the intense light from the image of the solar disk. After the occulter, all the optics in a coronagraph are shadowed from the bright sun and can have simple commercial grade polished surfaces to meet stray light requirements. A key decision in the design of the COSMO-LC was the selection of a reflective vs. a refractive O1 objective for the coronagraph optical system. A design trade is presented here where the result was the selection of a refractive optical system for the COSMO-LC due to the stray light advantages of a lens vs. a system.

Ground-based and Airborne Telescopes VI, edited by Helen J. Hall, Roberto Gilmozzi, Heather K. Marshall, Proc. of SPIE Vol. 9906, 990654 · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2235234

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx In this paper we will discuss scattered light from the optical surfaces of a reflecting and refracting optical system along with scattered light from dust on the optical surfaces. The performance of the COSMO-LC in terms of image brightness due to scattered light from the O1 over the field of view is presented. The design of the main O1 objective lens is pre- sented along with polishing and cleanliness requirements. An overview of the current PDR design of the COSMO-LC is also presented.

2. LENS VS. MIRROR

The trade between using a lens or a mirror is a very important one for an instrument with the stray light requirements of the COSMO-LC. Micro-roughness due to residual polishing defects (surface finish) and dust scatter light differently for a mirror and a lens. In this section we describe scattered light from surface finish on a mirror and a lens. We also de- scribe the effects of dust on a mirror and a lens and how dust increases scatted light. For the 1.5 meter COSMO-LC the cost of the lens would be significantly more than for a mirror, both in raw material and fabrication cost, another reason to carefully explore the lens vs. mirror selection of the objective lens for the COSMO-LC.

2.1 Scattering from surface finish

The discussion of scattered light from optical surfaces has been well described in the literature. Works by [6] describe a method of relating the surface Power Spectral Density (PSD) to the Bidirectional Scattering Distribution Function (BSDF) with units of 1/sr. This relation is given by Equation 1. The integration of the BSDF is the Total Integrated Scat- ter TIS.

Equation 1 BSDF(ß-ß0) = n S ( ) 𝟐𝟐 𝟐𝟐 �𝟒𝟒 𝝅𝝅 ∆ � 𝟒𝟒� 𝐜𝐜𝐜𝐜𝐜𝐜 𝜽𝜽𝒊𝒊 𝐜𝐜𝐜𝐜𝐜𝐜 𝜽𝜽𝒔𝒔 𝟐𝟐 𝒇𝒇 TIS = (𝝀𝝀ß-ß0) ß

The illumination wavelength is λ, is the incident angle,∫ 𝑩𝑩𝑩𝑩𝑩𝑩𝑩𝑩 is the 𝒅𝒅scattering angle, ß-ß0 is the difference between the specular and the scattering angles, and S ( ) is the two dimensional (2-D) PSD of the optical surface. ∆n is the differ- 𝑖𝑖 𝑠𝑠 ence between the index of refraction𝜃𝜃 between the two media.𝜃𝜃 For a mirror ∆n=2 and for a typical lens ∆n≈0.5. For the 2 COSMO-LC the incidence and scattering angles𝑓𝑓 are small, so the cosine terms and, are set to ~1 in Equation 1. The ß-ß0 relation is used because scatter is somewhat invariant to incidence angle. Scatter is determined from the specular 𝑖𝑖 𝑠𝑠 angle ß0. In our case ß0 0. The relation between BSDF and S ( ) in Equation𝜃𝜃 1 is valid𝜃𝜃 for surfaces where the RMS roughness is much less than λ. To apply the units used in this paper Equation 1 can be rearranged to give Equation 2 2 where the PSD S ( ) is≅ in units of (Angstroms^2 mm^2) and 𝑓𝑓is in units of Angstroms.

2 𝑓𝑓 𝜆𝜆 BSDF × n Equation 2 S ( )~ 𝟒𝟒 Å mm �×𝝀𝝀 � 𝟐𝟐 𝟐𝟐� 𝟒𝟒 𝝅𝝅 ∆ 𝟐𝟐 𝟐𝟐 𝟏𝟏𝟏𝟏 𝟐𝟐 𝒇𝒇 = sqrt( 𝟏𝟏S 𝟏𝟏𝟏𝟏( ) ) � �

The PSD, or S ( ) , is a quantity that can be measured𝝈𝝈 directly∫ 𝟐𝟐using𝒇𝒇 𝒅𝒅 𝒅𝒅a 2D interferometer. σ is the RMS surface rough- ness. The scale of features on the optical surface scatter light into angles that can be determined by the simple grating 2 equation. The BSDF𝑓𝑓 is a description of how a surface will scatter light through angle. The BSDF of a surface can be found directly by measuring how light is scattered off a surface through angle in an instrument called a scatterometer. These data can then be used to derive the 2-D Power Spectral Density (PSD) for the surface using equation 1. The term 4 n in Equation 1 becomes for a lens surface n=1.5, and 16 for a mirror surface. One can 2 2 2 2 see that for a given surface PSD a mirror will display ~8-10 (n 1.45-1.5) times more scattering than a lens due to sur- 𝜋𝜋 ∆ � 4 𝜋𝜋 � 4 𝜋𝜋 � 4 face� finish.𝜆𝜆 This� takes into account that� a lens𝜆𝜆 �has two surfaces where a mirror� has a single𝜆𝜆 � surface. The PSD is a physi- cal description of the optical surface and is wavelength independent.≅ The BSDF, or scattered light, has a 1

dependence. 2 � �𝜆𝜆 �

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx 2.2 Scattering from dust

To further explore the comparison between a lens and a mirror we look at how dust adds to scatter light in a lens and mirror optical system. In practice no optical system is free of dust and this is especially true for an instrument located at a remote mountain top. We used the Modeled Integrated Scatter Tool (MIST) software [7] to calculate the BSDF from particles on a mirror surface [aluminum, nreal= 0.902, i= 6.210] @ 532nm and a lens surface [lens, nreal=1.5, i=0]. Figure 1 shows the resulting BSDFs for a single 20µm spherical particle @ 532nm [dust, nreal= 1.5, i= .0002]. The size of the dust particle dominates the magnitude and shape of the BSDF for small scattering angles, not the particle index [8]. What is clear from Figure 1 is a particle sitting on a mirror scatters about 4 times more light than the same particle sitting on the surface of a lens. This is mainly due to the extra scattering paths from a mirror where the scattering paths add coher- ently for near normal incidence angles. The BSDF from a dust particle depends roughly on the diameter of the dust parti- cle to the 4th power, so scattering is strongly dominated by the largest dust particles on an optical surface.

0.1

0.01

0.001

1y 0.0001 -1vlirror -Lens (n=1.5) CO 0.00001

0.000001

Scatter angle (degrees)

Figure 1 BDSF for a 20μm diameter particle n=(1.5,0.0002) on a lens surface n=(1.5,0) and on a mirror surface n=(0.902,6.21). The surface area is 1X1cm. The calculation is for a wavelength of 532nm.

It was found that the 4X increase in scatter for a particle on a mirror surface applies to particles of all sizes in the range 1μm to 500μm that was checked using MIST. Larger size particles were not looked at because sizes larger than 500μm are easily seen by the eye and blown off the optic. For identical dust particle distributions, a mirror will scatter 2 times more light than a lens due to a lens having two surfaces compared to the mirror’s single surface.

2.2 Scattered light summary

In summary a lens has a significant advantage ~12 times the reduction of stray light over a mirror with all manufacturing and cleanliness levels being equal. We did not include the investigation of scattering due to coating defects on a mirror which we assume would also increase scattered light for a mirror. The COSMO-LC O1 lens will not have optical coat- ings to avoid scattering from coating defects, which also gives the lens another advantage over a mirror. It is clear to us that the COSMO-LC should use a lens for its main objective that is exposed to the full light of the sun. It will later be

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx shown in the next sections, where the design of the COMOS-LC’s main objective is given, that even a very well “super polished” and clean lens will have very little margin in observing the faint solar coronal emission lines. The goal for COSMO-LC is to keep the total stray light below 5 parts per million of the brightness of the solar disk at 1.1 solar radii from sun center at a wavelength of 1.0µm.

3. THE COMSO-LC O1 OBJECTIVE LENS DESIGN

In the past, coronagraph O1 were usually about 20cm in diameter and made from Schott BK-7 glass. In 2013 the HAO MK-IV coronagraph was replaced with the COSMO-K-Coronagraph that uses a new fused silica material, Corning C7980 HPFS. Programs such as the Large Synoptic Survey Telescope also use large lenses, 1.6-0.73 meters diameter, made from C7980 [8]. C7980 is made by an evaporative process which makes it very pure and defect free for making optical fibers for the telecommunication industry. The inclusion class is class-0 and the homogeneity is class-D (3 ppm) in a blank the size required for the COSMO-LC. This material has very low inclusions similar to BK-7 glass and polishes very similar to fused silica, which is harder than BK-7, making it easier to reach smoother surface finishes . The main requirement for a coronagraph O1 lens is to provide a low scatter image of the sun that has image quality well enough that an occulter can block the image of the solar photosphere with very little over spill of diffracted or scattered light. In the case of COSMO-LC low stray light is required beyond 1.05 solar radii. Design trades were made on the best F/ratio for the COSMO O1. The trades were based on image quality, F/ratio, and overall length of the COSMO-LC O1. A low F/ratio design has a shorter length, but has increased aberrations. An F/5.0 7.5 meter EFL design was finally chosen to be the best compromise between instrument length and image quality. Figure 2 shows a spot diagram for an all spherical F/5.0 and an aspheric F/5.0 COSMO-LC O1 lens.

OBJ: 0.2700 (deg) 0.6563 10000.00

Surface: IMA IMA: 35.083 mm Spot Diagram

4/26/2016 Units are µm. Field : 1 RMS radius : 1766.21 GEO radius : 3157.25 temp.ZMX Scale bar : 1e+004 Reference : Centroid Configuration 2 of 4

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx OBJ: 0.2700 (deg) 0.6563 300.00

Surface: IMA IMA: 35.343 mm Spot Diagram

4/26/2016 Units are µm. Field : 1 RMS radius : 18.054 GEO radius : 29.128 temp.ZMX Scale bar : 300 Reference : Centroid Configuration 2 of 4

Figure 2 Spot diagrams @656.3nm and 0.27 degrees off-axis for an all spherical surface O1 (top) and an O1 with one as- pheric surface (bottom). The scale bar is 10mm for the top plot and 0.3 mm for the bottom plot. Both designs are F/5.0 with an EFL=7.5 meters @ 750nm. Spherical design (R1=4166mm, R2= -18980mm). Aspheric design (R1=3967mm conic=- 0.798, R2=-24650mm). Both designs have a center thickness of CT=150mm.

From Figure 2 it is clear that an all spherical O1, while much simpler to polish to low scatter surfaces, will not image to sufficient quality to block the image of the sun down to 1.05 solar radii. The aspheric design forms an image of the sun with a blur circle of ~2.5 arc-seconds at the edge of the solar image (solar limb). The aspheric design has a conic term applied to the 1st surface of the lens which departs from spherical by 145µm (Figure 3). The greater the surface departs from spherical the more difficult it will be to polish to a super smooth low scatter surface. The other side of the O1 as- pheric lens design is spherical. There O1 lens will also require a small amount of local figuring to account for the 3ppm index variation of the Corning C7980 glass. The O1 has a center thickness 150mm, so a 3ppm index variation would amount to about a maximum path variation of 0.6µm or a small figure correction on order 1 wave. This could be applied to either surface, but applying it to the aspheric front surface would keep the rear lens surface spherical and easier to polish. It should be noted that a 1.5 meter F/5.0 mirror with a spherical surface will image the sun’s limb to a blur circle of ~28 arcsecond, so a mirror O1 can remain spherical for a COSMO-LC.

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Figure 3 A plot of the departure from “best fit” spherical vs. radial position for the COSMO-LC aspheric lens design. The max departure is 145µm.

4. SURFACE FINISH AND CLEANLINESS REQUIREMENTS FOR THE COSMO-LC O1

4.1 Surface finish The COSMO-LC will view the solar corona from 1.05 solar radius (50 arc-seconds) out to 1 solar radius (0.25 degrees) above the solar limb, therefore it is important to minimized light scattering for angles 50 arc-seconds to 0.75 degrees. The 0.75 degree requirement is due to light that is scattered from the opposite side of the solar image across the 0.5- degree sun out to 0.25 on the other side of the field. Applying the grating equation with the longest wavelength the COSMO-LC will observe (1.0µm), and the smallest scatter angle of 50 arc-seconds sets the maximum scale length of surface features on the O1 that can scatter light beyond 50 arcseconds, which corresponds to features 4 mm in size. Ap- plying the grating equation again with the shortest wavelength (.53µm) and the largest scatter angle of 0.75 arc-seconds sets the minimum scale length of surface features on the O1 that can scatter light inside 0.75 degrees, which corresponds to features 0.04 mm in size. The surfaces of the COSMO-LC lens must be smooth over scale lengths 4-.04mm (0.25-25 (1/mm).

To put Equation 1 into practice the Harvey Shack BSDF model (K-correlation model) is used which is given by Equation 3.

s 2 2 BSDF( )= 1+ ß-ß0 Equation 3 ß-ß0 b0 � � � � 𝑳𝑳 � � b0 is the specular BSDF value. ß0 is the incident ray angle. ß is the scatter angle (see equation 1 ), L is where the BSDF rolls off to avoid a singularity at ß-ß0=0, and s is the slope. For our case ß0 can be set to 0 since we are describing scat- ter for basically on-axis rays <1 degree off-axis. Equation 3 can be integrated in closed form using equation 1 to give RMS . The RMS surface roughness σ will be given to the optical company fabricating the O1 to set surface finish re- quirements2 on the COSMO-LC O1 over spatial lengths (4-.040mm). The closed form integration of this equation is giv- en by 𝜎𝜎Equation 4.

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx L log + = n L 𝝀𝝀 𝟐𝟐 𝒃𝒃𝒃𝒃 𝟏𝟏 Equation 4 = 𝟐𝟐 (S ) (S ) 𝟐𝟐 𝟐𝟐𝟐𝟐 𝝅𝝅 𝒆𝒆 𝟐𝟐 � � � �S �(𝟏𝟏 + L �) (L ) 𝐟𝐟𝐟𝐟𝐟𝐟 S𝐒𝐒 −𝟐𝟐 n 𝟐𝟐 L (S ) +𝟐𝟐 +𝟐𝟐 𝝈𝝈 � 𝝀𝝀 𝒃𝒃𝒃𝒃 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝜟𝜟 𝟐𝟐𝟐𝟐 +𝟐𝟐 To describe scattering as close in as 50 arc�-seconds� � the BSDF� � 𝟏𝟏 model is allowed− to roll� off at𝐟𝐟𝐟𝐟 angles𝐟𝐟 ≠ −slightly𝟐𝟐 less than 50 arcseconds, so L is set to L=.0002 radians. Inside 50 arcseconds scatter is held constant to avoid an on-axis singularity. S is set to S=-2 to describe a good super polish where the BSDF falls off with a slope of -2 in log-log space. Then b0 is set to scale the BSDF to a value for σ, the RMS surface roughness, using Equation 4. Figure 5 shows three PSD curves that describe a surface finish of 5, 10, and 20 Å RMS. The functional forms of the PSDs are identical to Equation 3. Since the model BSDF was designed to roll off at L=.0002 the PSD also rolls off at a spatial period of 1 d = L or d = 5mm. Numerical integration can be performed between the spatial periods shown in Figure 4 to derive the exact require- ment for σ. This value of σ will be slightly less than the full integration value given by Equation 4. ⁄ ⁄𝜆𝜆

1000

PSD 5A RMS 100

N 10 - - PSD 10A RMS

E -PSD 20A RMS E N 0.1

0.01

0.001

I 1 1 1 1 1 1 1 i 1 1 i i i 0.0001 1 1 1 1 1 1 i'i'1 l 0.1 1 10 100 1 /mm

Figure 4 PSD curves @ 1µm for a 5, 10 and 20A RMS surface. The fit parameters using equation 3 are (5A RMS [b0=1.26 L=.0002 S=-2]) (10A RMS [b0=5.03 L=.0002 S=-2]) (20A RMS [b0=20.1 L=.0002 S=-2]). The vertical lines represent the spatial periods of interest to COSMO-LC 0.25-25 (1/mm).

Having a PSD curve that rolls over at longer scale lengths, > 4mm, does not eliminate figure requirements for the longer scale lengths of the lens surface. For example, features on the lens surface that are ~10 cycles across the lens (~150mm for COSMO-LC) will scatter in the ~ 1 arc-second range, well behind the 50 arc-second oversized occulter. The lens surface still needs to have good figure over large scale lengths, but achieving good image quality is an easier requirement than achieving stray light below a few parts per million. For example the lens surface specification is ~1/4 wave Peak-to- Valley at 6328Ånm or about 350Å RMS which is much larger than ~5-20Å RMS.

To model stray light we used FRED optical software from Photon Engineering (Tucson, AZ). The Harvey model BSDF parameters b0, L, and S can be entered directly into FRED to geometrically trace rays and statistically “scatter” the rays according to the BSDF function, similar to an analysis by [9]. A model of the aspheric COSMO-LC O1 lens using pa- rameters given in Figure 2 was created in FRED using Corning C7980 fused silica for the lens material. A grid of 300X300 rays was placed at the O1 pupil. These rays were assigned a random direction from 0 to ±0.26 degrees to mod- el the solar disk which subtends 0.52 degrees in diameter. The rays are then traced through the O1 lens. After refraction at each lens surface a single ray is then multiplied into 300 rays, to increase calculation efficiency. Small angular pertur- bations are added to each ray’s angle where the perturbation of the ray is determined statistically by the BSDF model

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx entered in FRED. The size of the 300X300 grid and the 300 additional rays applied to the scatter calculations are param- eters that were determined when by adding additional rays resulted in a minimal increase in the calculated intensity of the scattered rays, the number of scattered rays reached an asymptotic value. An additional feature in FRED is that “im- portance-zones” can be created to preferentially direct the rays to a sensor or optical focus to make the simulation more efficient. Scatter is not randomly simulated over 2π, which would be very inefficient. FRED handles the statistics of the importance-zones, so the results are correct and simulate real scattering of light rays with shorter ray trace times. The rays are traced to the focus of the O1 lens where most of them fall inside a circle which simulates a disk “image” of the sun. The ray data set is analyzed for the number rays per unit area that strike the sensor beyond the disk image (irradi- ance). To display the data in terms useful for the COSMO-LC project the ray density that forms the disk image of the sun is normalized to an irradiance=1. This scales the density of rays that strike beyond the disk image to fractional units of ray density inside the disk. Figure 5 shows the results where the scale has been changed from an irradiance of 1 to the brightness of the sun Bo. The COSMO-LC stray light requirement is <5 millionths at 1.1 solar radii at a wavelength of 1.0µm, so it is obvious from Figure 5 that the surface roughness of the COSMO-LC needs to be < 20A RMS. We will now look at scattering levels due to dust in the next section followed with derivations for the specifications for surface roughness and cleanliness level of the COSMO-LC O1.

1.00E -04

1.00E-05

1.00E -06 SARMS . 10ARMS '.... 20ARMS ...'" ...... 1.00E-07 ..:.....s

1.00E -08 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Solar radii from sun center (Rsun)

Figure 5 Scattered light @ 1µm derived with the FRED optical model for the O1 for surface finishes of 5, 10, and 20A RMS over spatial periods of 0.33-25 (1/mm) @ 1.0µm. The HS fit parameters are (5Å RMS B0=1.26 L=.0002 s=-2), (10 Å RMS B0=5.03 L=.0002 s=-2), (20 Å RMS B0=20.1 L=.0002 s=-2).

4.2 Scattering from dust particles on the COSMOS-LC 01

In this section we describe scattering by dust particles on the COSMO-LC O1. The MIL-1246C specification describes a distribution of dust particles by size and count. The basic MIL-1246C equation is shown in Equation 5 which describes the number of dust particles of a given size per square foot.

Equation 5 Log(N)=s [Log2x Log2x]

Where N is the total particle count, x1 is the cleanliness level, s is𝟏𝟏 an− empirical slope factor (s=.926), and x is the particle size in microns. The particle size x varies from a minimum particle size of x=1µm up to the cleanliness level x=x1(µm). Setting a cleanliness level of x1=300 and x=300 µm in Equation 5 shows that there is one 300µm particle per square foot for a cleanliness level 300 surface. To model scattering from dust a BSDF is derived using MIST for a single sized parti-

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx cle, similar to what was presented in section 2.2. To derive the full dust BSDF a range of particle sizes is defined using bins di of width Δµm defined as follows [10].

di = 1 + ( 1/2) ); = 1,2, … Nbins

𝑖𝑖 − Δ 𝑖𝑖 Where Nbins is the total number of bins. The number of particles per square foot in each bin is then given by

s Log2[ ( ) ] s Log2[ ] Equation 6 fraction(di)=Ntotal − 𝟏𝟏+ 𝒊𝒊−𝟏𝟏 Δ − 𝟏𝟏+𝒊𝒊Δ s Log�𝟏𝟏𝟏𝟏2 x − 𝟏𝟏𝟏𝟏 � Where Ntotal=10 1 The BSDF for a single sized particle is then multiplied by the number of dust particles in the bin. This is performed for each range of particle sizes to derive the dust scattering BSDF. Figure 6 shows the BSDFs for cleanliness levels 100, 200, and 300 @ 1µm with a particle index n=1.5. These cleanliness levels represent a typical surface in a very good clean room. Similar to surface finish the Harvey BSDF model can also be applied to fit the dust BSDFs. Also shown in Figure 6 are the Harvey model fits parameters to each BSDF level.

Figure 6 BSDF from dust (n=1.5) on a lens surface (n=1.45) at cleanliness level 100, 200, and 300 @ 1.0µm wave length. Also shown are the HS fits to each level. (Level 300, B0=0.45, L=0.006, s=-2.15), (Level 200, B0=0.06, L=0.0065, s=- 2.15), (Level 200, B0=0.0022, L=0.0095, s=-2.3).

The Harvey model fit parameters were entered in the FRED optical model. A stray light analysis similar to the analysis in the last section for scattering from surface roughness was performed. The results are shown in Figure 7. The results show that to maintain scattered light at or below 5 millionths of the solar disk brightness the COSMO-LC O1 lens sur- faces must be maintained to better than MIL-1246C cleanliness level 300.

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx 1.00E -04

.- 1.00E-05 CO C VJ O

= 1.00E-06

Level 200 .iCIO - Level 100

CL1

fC aJ 1.00E-07

1.00E -08 1 1.1 1.2 13 1.4 1.5 1.6 1.7 1.8 1.9 2 Radial Distance (Rsun)

Figure 7 Brightness vs. radial distance due to scattering @ 1µm from dust on the O1 lens. A cleanliness level of 200 has about 3 millionths scatter at 1.1 solar radii in the image plane of the O1.

A unique set of data that HAO has collected over the years was a daily analysis of the stray light in the Mark IV white light coronagraph [11]. The data were collected from 2003-2011. These data showed that the Mark IV had the lowest stray light right after the Mark IV O1 lens was cleaned. The Mark IV O1 lens was periodically cleaned every few months. It was noted that the accumulation of dust on the Mark IV O1 lens over time contributed more scattered light than scattered light from the lens surface finish. The conclusion to make from this is making the O1 lens polish smother will only reduce stray light for a short period soon after the O1 lens is cleaned. It would be impractical and risky to per- form a through daily cleaning of the O1 lens. Typically what is done is the O1 lens is blown off every day which re- moves the larger dust particles, so in reality the exact model for dust on the O1 lens is probably some form of a truncated MIL-1246C cleanliness level. For the work presented here we only use the MIL-1246C dust model and combine those results with results from surface roughness to derive an overall specification for the polish and cleanliness level of the COSMO-LC O1. We have collected data at the Mauna Loa Observatory with particle counters to determine more quanti- tatively the dust conditions at the Mauna Loa [12]. These data will be used to further refine our knowledge of dust at Mauna Loa to aid in deriving better models for dust distributions and more accurate prediction of scattered light.

4.3 O1 specifications

From the analysis presented we can now derive detailed specifications for the COSMO-LC O1 lens polish and cleanli- ness level requirements. The requirements for stray light in the COSMO-LC is set at 5 millionths the brightness of the sun at 1.1 solar radii from the sun. No detailed cost trade analysis has yet been performed on lens polishing and on com- plicated purified air systems. For now, we see pushing either requirement driving up costs substantially. So we decided to split the contributions of scattered light equally between surface finish and dust where each parameter contributes 2.5 millionth for a total of 5 millionths at 1.0µm. The specifications to achieve this level of scatter are given below along with their Harvey BSDF model parameters.

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx O1 Lens Surface Finish 11.7A RMS over .25-25 1/ mm spatial periods HS parameters B0=6.85 L=.0002 S=-2

O1 Lens Cleanliness Level MIL-1246C Cleanliness level= 188 HS parameters B0=.047 L=.0072 S=-2.28

The surface specification for the O1 will be challenging to meet because of the long 4mm spatial length the surface finish applies over. Typically optics houses will quote an RMS surface roughness of say 5 or 10 angstroms RMS without any reference to spatial scale length. These specifications are usually implied to be over very small spatial periods < ~1mm, making these specifications much easier to achieve. The cleanliness level of 188 should be capable of being met with conditions at Mauna Loa since HAO currently has two operational coronagraphs that have demonstrated low scatter. Scattering from dust particle distributions is invariant to the size of the optic, so current conditions at Mauna Loa apply to a 1.5 meter O1.

4.4 COSMO-LC optical system overview

The overall layout of the COSMO-LC optical system is shown in Figure 8, and a closer detailed view of the aft optics section is shown in Figure 9. The COSMO-LC will operate with its filtergraph from 530-1083nm, but he C7980 O1 material will allow for instrumentation to work out in the IR to ~2.0µm. The optical parameters of the COSMO-LC design are given in Table 1.

Lyot Filter pair + Sensors

1.5m 01 Lens

Figure 8 Overview of the COSMO optical layout. The instrument will have a total track of ~9.4 meters. The instrument is dominated by the large 1.5 meter O1 lens.

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx Band Pass Lyot Filters Sensor Lens #3 filter Lenses #1, #2 Lens #4 Lens #5 1 L/ pair \ - . II I Sensor

Lens #6 Polarizing Occulter Lenses #7 -11 Beam Splitter 01 focus Lyot Stop Modulator

Figure 9 Detailed view of the occulter, AFT optics, and Lyot filters.

Table 1 COSMO-LC design and performance parameters.

Wavelength coverage 530-1100 nm (filter graph) Aperture 1500 mm Field of view 1 X 1 degree 1st EFL 7500mm F/5 Final EFL 3419mm F/2.3 Sensor HgCdTe 4K X 4K pixels Pixel size 15µm IFOV 0.9 arc-seconds Ensquared Energy >84% inside 2X2 arc-seconds Parameters are for 656nm. Other wavelengths vary slightly.

All the lenses have had their sizes carefully specified so they meet the glass materials that Ohara and Schott glass can provide. The maximum diameter for some of the glasses was limited to diameters of 180mm. All the optics in the design use simple spherical surfaces except for the O1 lens. All the lenses, except for the O1 lens, will be broadband anti- reflection coated. A brief description of the COMSO coronagraph optics follows.

After the O1 is the occulter. The occulter will have to be variable in size to account for the seasonal changes in the ap- parent size of the sun and changes in the effective focal length of the singlet O1 due to axial chromatic aberration. Figure 10 shows a design concept for the occulter that can vary in size.

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx Primary blades Main (fixed) body Drive disk 110 elmOa sea %JIM,/ t1 ‘Back’ blades

Figure 10 Illustration of the variable occulter concept. The solar image is ~70mm diameter.

The occulter will have to have a cooling system to remove heat because there will be ~2.1kW of energy in the solar im- age incident on the occulter. We have studied water cooling and cooling by heat pipes to keep the occulter to ~65C.

After the occulter are six lenses, 1-6 shown in Figure 9. These lenses form an image of the O1at the Lyot stop. In op- eration the image of the O1 is surrounded by a bright ring of light at its edge and a much dimmer spot of light at the cen- ter of the image. These features are due to diffraction at the O1 aperture stop and the obscuration by the occulter at the 1st image. The light in the bright ring amounts to ~100 millionths the brightness of the sun. Blocking this light is the key of the Lyot coronagraph design. The Lyot stop is variable in size and is sized slightly smaller (~90%) than the diameter of the bright ring [2]. The much weaker central spot of light is eliminated by adding a small disk to the center of lens#7 which is located behind the Lyot stop.

Following the Lyot stop are another set of lenses (lenses 7-11) in Figure 9 that form the final image of the sun. Light from these lenses passes through an additional set of non-powered optics used to analyze the wavelength and polariza- tion nature of the light from the corona for measurements of coronal magnetic fields.

The first non-powered optic is the band pass filter which isolates a narrow band of light centered on a spectral line (~1nm FWHM). The out of band performance of this filter is critical to the operation of the coronagraph [13]. The oc- culter can only be focused and sized for one wavelength. The other wavelengths that are bluer will focus to a shorter focal length and the redder wavelengths will focus to a longer focal length. This allows light from the bright solar image at other wavelengths to “spill” past the occulter. The band pass filter will need to block this light to a level of ~1 × 10 . The HAO coronagraphs in operation have custom design band pass filters that block out of band light to this level. An-−5 other important aspect of the design of the band pass filter is its size which is 160 mm in diameter. This is very large for a filter with a pass band on order 1nm FWHM.

The next non-powered optic is the modulator which is used to modulate the Stokes parameters (I, Q, U, V) of the incom- ing polarized light from the corona. In the COSMO K-Coronagraph this optic is made from ferroelectric liquid crystals (FLCs). It is not clear if FLCs can be made in the 150mm diameter range COSMO-LC requires. It is possible that this optic can be made from rotating achromatic waveplates which are manufacturable in sizes >150mm diameter from poly- carbonate plastic laminates.

The polarizing beam splitter (PBS) cube is located after the modulator and will reflect and transmit orthogonal polariza- tions to each of the two Lyot filters. This setup allows for simultaneous observations of the sun in the orthogonal polari- zation states to eliminate seeing effects in the polarization analysis of the signal. The PBS is 140X140X140 mm and made out of common SF11 glass. We have looked into several design options for the PBS’s active polarization splitting surface. One approach is to use a dielectric multilayer coating. We have found that this design approach suffers from

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx limitations due to angle sensitivity. The angle of the chief ray through the COSMO-LC PBS is ~±12 degrees and a PBS with a dielectric multilayer coating can only accept ~±2 degrees. Another concept that offers more promise is to use a wire grid polarizer. The wire grid polarizer is very insensitive to beam angle and can operate over the full wavelength range of the COSMO-LC. Wire grid polarizers are typically made on thin ~0.7mm thick double-sided polished fused silica wafers. These thin wafers can be cut and optically contacted to the prism hypotenuse. Since the wafer surfaces are very parallel the reflected surface of the wire grid polarizer should closely match the surface of the flat prism hypotenuse after optical contact. Wire grid polarizers typically have low contrast (~<1:10) in portions of the spectrum for the reflect- ed S-polarization beam, so a cleanup polarizer could be used to increase contrast.

The identical Lyot filters are key components to the COSMO-LC filter graph. A through discussion of the COSMO-LC Lyot filter is presented in [14], we present only a top overview here. Unlike most Lyot filters which use calcite for the birefringent material the COSMO-LC filter graph will use lithium niobate (LiNbO3) birefringent crystals. LiNbO3 has about half the birefringence (~0.08) of calcite (~.17) and has a very high index of refraction n~2.2. The 5 stage Lyot fil- ter will have a FWHM of ~0.1nm at 1.0µm using two 22mm thick LiNbO3 crystals for the thickest wide field element. The acceptance cone for this filter is a ~36 degree cone which allows the filter to operate in the F/2.3 beam of the COS- MO-LC final focus. The aperture of the COSMO-LC Lyot filter is 100mm which is larger than any Lyot filter that uses calcite. LiNbO3 is commercially grown in boules currently up to 150mm in diameter. The largest aperture calcite filters have apertures ~40mm. LiNbO3 is electro-optic, so the filter will be tuned by applying an eclectic field across the LiNbO3 plates [14].

4.5 Operation of the COSMO-LC

The COSMO-LC achieves its wide wavelength range of operation through focus compensation of it optical components. There are three optical groups in the COSMO-LC design where focus compensation is used. The compensators are the distance between the O1 and the occulter, the distance between lens#6 and the Lyot stop, and the distance between the sensors and the Lyot filters (final focus). These changes in spacing are additive in the sense that any change in spacing between the O1 and the occulter requires that the occulter and all the optics aft of the occulter to move relative to the O1. Then on top of that motion the Lyot stop and all optics aft of the Lyot stop must move position relative to lens #6. Then finally the sensor changes position relative to the Lyot filter for final focusing. This can be achieved by putting all the optics aft of the occulter, on a stacked three stage system shown schematically in Figure 11. Table 2 shows the nominal spacing for the three compensators for three select wavelengths of 530nm, 635nm, and 1083nm.

To 01

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111111111111111111¡iiiiiiiiiiiiiiii11111111111iá11111iñími111iiim ririñ iiiiiiiiiiiiiiiiiiii1iii11111

IIIIIIIStage 1 ®Stage 2 M Stage 3

Figure 11 The COSMO-LC focus stages. Note there are no optic change outs to configure the COSMO-LC to work from 530-1083nm. The spacing between the O1, (occulter+all optics aft of the occulter) move as much as ~180mm on stage 1. The Lyot focus and all optics aft of the Lyot stop move as much as ~15mm. The spacing from the Lyot filters to the sensors moves as much as ~3.5mm.

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Wavelength 530nm 656nm 1083nm O1 to occulter (sun focus) 7338.9mm 7410.82mm 7527.00mm Lens #6 to Lyot stop (O1 focus) 30.791mm 37.642mm 45.930mm Lyot filter window to Final focus 48.452mm 44.903mm 44.917mm Table 2. Nominal focus spacings used to operate COSMO-LC

4.5.1 Final focus performance of filter graph (530–1083nm)

Figure 12 shows the RMS spot sizes the final focus of the COSMO from 530-1083nm. One can see the COSMO-LC design meets performance requirements from 530-1083nm using a 15µm pixel sensor at the final focus.

4.0

3.5

3.0

2.5

2.0 Final focus

1.5

1.0

0.5

0.0 530 630 730 830 930 1030 Wavelength (nm)

Figure 12 The RMS spot size of the COSMO-LC RMS final focus (~3400mm EFL) as a function of wavelength at a field angle of 0.27 degrees (limb of sun). This plot was generated while applying the focus motions described in the prior section. The COSMO-LC design will meet imaging requirement from 530-1100 nm for the filter graph which will have 15µm pixels.

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx 5. CONCLUSION

We find that a lens has significant advantages over a mirror in terms of surface roughness and cleanliness require- ments to provide a low scatter image of the sun. The requirements for a lens are over an order of magnitude easier to achieve than for a mirror in terms of surface finish and cleanliness requirements required for the COSMO-LC. In the past BK-7 glass was the best choice for the O1 lens due to its minimal inclusions and low striae. We have found that Corning C7980 HPFS to be a better material for the O1. C7980 has a low CTE and hardness similar to fused silica making it better for polishing a smooth surface over BK-7. The O1’s aspheric surface departs from the best fit sphere by145µm. This presents the biggest challenge to achieving the surface roughness requirements. The surface requirements for the COSMO-LC are not much different than for X-ray optics, which have much more complicated non-spherical surfaces, so fabrication of the O1 is within current technology.

We have presented an overview of a design for a 1.5 meter Lyot coronagraph. There are key parts of the COSMO- LC design that will require further work such as the PBS and modulator components. The Lyot filter is currently undergoing development to allow it to operate from 530-1100 nm. The COSMO-LC achieves it wide wavelength range of operation through the use of variable positions of its optical components similar to the operation of a zoom lens. The COSMO-LC will have the capability to operate at wavelengths beyond 1.0µm which is only limited by the spectral transmission of the Corning C7980 material.

6. REFERENCES

[1] Gallagher D., Tomczyk S., Zhang H., Nelson P., Proc. SPIE 8444, Ground-based and Airborne Tele- scopes IV, 8444-3P (2012); doi:10.1117/12.927155

[2] De Wijn A., Burkpile J.,Tomczyk S., Nelson P., Huang P., Gallagher D., Proc. SPIE 8444, Ground- based and Airborne Telescopes IV, 8444-3N (2012); doi:10.1117/12.926511

[3] Tomczyk, S., Card, G.L. Darnell, T., Elmore, D.F., Lull, R., Nelson, P.G., Streander, K.V., Burkepile, J., Casini, R., and Judge, P.G., “An Instrument to Measure Coronal Emission Line Polariza- tion.” Solar Physics, 247, 411-428 (2008).

[4] Nelson P., Tomczyk S., Elmore D., Kolinski D., Proc. SPIE 7012, Ground-based and Airborne Tele- scopes II, 701231 (2008); doi: 10.1117/12.789494

[5] See the Technical Notes section of the COSMO web site (www.cosmo.ucar.edu).

[6] Stover, J. C., Optical Scattering: measurements and analysis, SPIE Press, 179-180 (1995)

[7] Modeled Integrated Scatter Tool (MIST - v.2.10) developed by Dr. Thomas A. Germer at the Optical Technology Division of the National Institute of Standards and Technology in Gaithersberg, MD Software is free for downloading at the NIST Optical Technology Division web site (http://physics.nist.gov/Divisions/Div844/facilities/MIST/mist.htm).

[8] LSST Camera Design, Oliver S., Riot V., Gilmore D., Bauman B., Pratuch S., Seppala L.,Ku J., Nordby M., Foss M., Antilogus P., Morgado N., Sassolas B., Flaminio R., Michel C., SPIE Proceedings 8446, Ground-based and Airborne Instrumentation for Astronomy IV, (2012) 84466B-1; doi: 10.1117/12.926710

[9] Hubbard, R., “M1 Microroughness and Dust Contamination, ” Advanced Technology Solar Telescope Technical Note No.0013, Rev. C

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/10/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx [10] Johnson B.R., Arnold G.S., Radiation Scattering from Particulate contamination , AERO- SPACE REPORT NO. ATR-94(7281)-1, (1994)

[11] Elmore, D.F., (2007), “Mk IV scattered light analysis”, Technical Note 10, COSMO web site www.cosmo.ucar.edu.

[12] Tomczyk, S., (2015) “COSMO Site Cleanliness Report“, Technical Note 24, COSMO web site www.cosmo.ucar.edu.

[13] Tomczyk, S.,(2010) “Chromatic Aberration in a Singlet Coronagraph Objective Lens “, Technical Note 3, COSMO web site www.cosmo.ucar.edu.

[14] Tomczyk S., Mathew S., Gallagher D.,”Development of a Tunable Filter for Coronal Polarimetry” , Journal of Geophysical Research, (2016-submitted)

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