SOW.pdf

1 Scientific,Technical, Management Section

1.1 Introduction

Pathways to Discovery in Astronomy and Astrophysics for the 2020s, the ASTRO2020 Decadal Survey, lays out an ambitious suite of programs to address key 21st century as-trophysics. Within the New Messengers and New Physics theme, ASTRO2020 identifies What physics drives the cosmic expansion and large-scale evolution of the universe? as one of the key science questions, further noting that The unknown physical natures of dark mat-ter and dark energy, both discovered through astronomical measurements, remain outstanding grand challenges in both physics and astronomy.

Type Ia Supernovae (SNe Ia) measurements led to the discovery of the accelerating expansion of the Universe (Perlmutter et al., 1999; Riess et al., 1998), attributed to dark energy. Subsequent measurements using Weak Lensing (WL), Baryon Acoustic Oscillations (BAO), Galaxy Clusters (GC), and SNe Ia in visible and near infrared wavelengths, and microwave experiments with WMAP and Planck, confirmed the original discovery, leading to the current concordance model, ΛCDM , that assumes a cosmological constant for dark energy, a flat universe and cold dark matter. However, a key goal in cosmology is to test for deviations from the cosmological constant model to the practical limits of available methods ... as such deviations would be a signature of new physics or reveal a breakdown of general relativity (GR) at large scales.

Requirements for Stage-IV Dark Energy Experiments The Dark Energy Task Force (DETF) outlined Figure of Merit (FoM) requirements for successive stages of dark energy experiments that utilize WL, SNe Ia, GC and BAO, (Albrecht et al., 2006). Each successive stage must achieve a higher value of the dark energy FoM, defined to be the reciprocal of the area of the ellipse enclosing the 95% confidence limit in the w0–wa plane;

where the dark energy equation of state is parametrized as w(a) = w0 + (1 − a)wa, and w0 is the present value of w (ratio of pressure to energy density), and wa is the linear time evolution of w(a), where a is the size of the universe relative to its current size. In this

(a) (b)

Figure 1: (a) Differences from ΛCDM as a function of redshift if there is a 1.5% shift in the value of w0 or if the value of wa changes by 7%. Maximum difference is 6.4 mmag (∼ 0.6%) (From B. Rose). (b) The largest sources of systematic uncertainty in the SNe Ia figure of merit are flux calibration and detector non-linearity. The vertical dotted lines at the left side of each bar is the FoM based on current calibration uncertainties. (Hounsell et al., 2018).

context, cosmology with the Roman Space Telescope (and Rubin Observatory) represent Stage-IV experiments, and require FoM values more than 10× larger than Stage-II studies.

Combining methods yields a higher FoM over that of a single probe.

For Stage-IV SNe Ia cosmology surveys to meet their science FoM objectives (e.g. FoMSNe = 325 for Roman) they require stringent control of systematic sources of uncertainties. Distin-guishing between deviations from the standard ΛCDM model, as shown in Fig.1a at the few millimag level illustrates this point. For SNe Ia the most significant systematic uncertainties arise from flux calibration (Hounsell et al., 2018; Brownsberger et al., 2021), thus the quality of the calibration standards limits the accuracy. Figure1b shows the impact of improving calibrations on the SNe Ia FoM. Specifically, the references used to carryout flux calibrations need to be accurate to better than 0.4%, with a goal of 0.2%, to accurately compare fluxes in the rest-frame wavelengths between science targets at high and low redshift. This is a factor of 2-5 better than achieved by current missions in the visible and approximately 10× better than currently available in the near infrared, (Bohlin et al., 2020).

Two general approaches to establishing fundamental flux calibrations at the telescope, i.e.

system throughput versus wavelength, are 1) to use stars whose spectral energy distributions are accurately determined and 2) to project a calibrated light source into the instrument.

Stars as Flux Standards. The advantage of using stars as flux calibrators is that they are always available in the sky, and, if they are calibrated against physical standards provide SI-traceability. However, only a very few stars, e.g. Vega and Sirius, claim such a pedigree (Hayes et al., 1971; Hayes & Latham, 1975; Price et al., 2004), and even then lack full wavelength coverage between 0.35 – 2.5 μm: spectroscopy between 0.35 - 0.9 μm , broadband photometry in the near and mid-IR, and/or unacceptably large uncertainties (Mountain et al., 1985a,b; Selby et al., 1983; Blackwell et al., 1986). Furthermore, these stars are far too bright to be observed by most telescopes without saturating. An alternative is to use stellar atmosphere models of fainter white dwarf (WD) stars, normalized at 5556 Å to Vega. This is the approach used to establish the CALSPEC system (Bohlin et al., 1995, 2014, 2020), as the atmospheres of hot WDs are “easy” to model, compared to most spectral types, as they have few spectral features. The uncertainties in this approach are limited by the accuracy of the stellar models, how well different models agree with each other (see Fig. 2) and the underlying errors due to the original Vega flux calibration.

Dissecting this, we face the following situation. First, the WD models rely on determi-nations of effective temperature (Teff) and surface gravity (g) from Balmer line profiles of stars that are known to be unreddened. Second, choices of the input physics, viz. local ther-modynamic equilibrium (LTE) or non-LTE (NLTE), atomic species, metallicity, etc., affect the model output spectra. Although Bohlin et al. (2020)’s updated models for CALSPEC’s primary WDs (GD153, GD71 and G191B2B) result in impressively small uncertainties–1-σ uncertainties of ∼0.5% relative to 5556 Å (between ∼0.5 and 10 μm)–this is really the level of agreement between different generations of models. It does not indicate the accuracy of the models vis-á-vis the stellar SED. Third, photometric systems are still based on the 40+year old measurements of Vega’s spectral irradiance, whose uncertainty is limited by systematic effects (known, but poorly quantified), particularly in the infrared. The uncertainty in the calibration scale of the current standard star systems is at best 1% (cf. Megessier (1995)).

The accuracy of the absolute flux level is important for determining fundamental stellar parameters (mass, size, temperature), and for cosmology, it is the uncertainty in the true flux vs. wavelength runout (”the slope”) that must be small - 0.4%, in order to compare rest-frame flux of high redshift to low redshift targets. SI-traceable physical flux calibration of stable stars provides one way out.

0 2 4 6 8 10

0 2 4 6 8 10 Wavelength (micron)

U nc er ta in ty

555.6 nm J

H

K

Absolute color target: 0.4%

MSX B1

MSX B2 MSX A

(a) (b) (c)

Figure 2: (a) Uncertainty in Vega’s absolute fluxes. Filled diamonds are pre-1990, ground-based, J,H,& K fluxes determined from black body furnaces or the Sun, and for 5556Å

cf. Megessier (1995). Not shown is the 10% uncertainty in the L band at 3.8μm. Filled squares are uncertainties for space-based (1996) calibrations with MSX (Midcourse Space Experiment), Price et al. (2004), demonstrating that a space-based calibration system can attain the needed accuracy. (b)Improving the flux calibration accuracy, increases the FoM.

At a calibration accuracy of 0.4% the relative FoM gain 1.9×, and for our goal of 0.2%, the gain is 3.6×. (c) Impact of improved accuracy on the w0-wa confidence interval for joint LSST-Roman analysis.

Projector Systems. In this method, an artificial star or projector system is used to inject light into the telescope, where NIST-traceable photodiodes or electrical substitution radiometers calibrate the light being injected. Although several ground-based projector system are under development (e.g., Lombardo et al., 2014, 2017; Coughlin et al., 2016, 2018)), none of these is able to fully illuminate the telescope pupil in the same way as an astrophysical source at infinity. In addition, ground-based artificial star systems have a line of sight to the telescope that is subject to extinction that is unlike that experienced by celestial sources, and is more time-variable (e.g., due to blowing dust, pollen, etc.). Correcting for the horizontal extinction is entirely different than for the ‘vertical’ atmospheric extinction of celestial objects. These factors are serious challenges to achieving a calibration accuracy of 0.4%, much less 0.2%.

A solution to the need for accurate telescope calibration is an artificial star above the terrestrial atmosphere with SI-traceability.

Calibrating an Observatory with an Artificial Star. The light emitted from the artificial star illuminates the telescope aperture, is directed through the entire optical path and the measured signal, S, is recorded. The irradiance (spectral energy density), FC(λ), of the emitted light is known so the relationship between FC(λ) and S can be determined:

FC(λ) = R(λ)×S, where R(λ) is the wavelength-dependent system throughput (responsivity

Item Requirement SI Traceability Knowledge of emitted flux is ≤0.4% with a goal of 0.2%

Exit beam profile smooth and stable such that the ratios of fluxes between wavelengths is the same at the entrance pupil of the receiving telescope as at the on-board SI-traceable flux monitor(s)

Emitted flux 10 - 105 photons m−2 s−1 in a monochromatic line.

Wavelengths Minimum 3 wavelengths between 0.35 and 2.3 μm Power < 125 Watt Mass: < 10 kg Volume: < 12U (2x3x2)with target volume ≤ 6U (2x3).

Surface contamination Must be monitored and characterized Risk Low

Stray Light Control sufficient to retire any risks in achieving 0.4% flux knowledge

Radiation Tolerance Net impact ≤ 0.2%

Table 1: Artificial star flight requirements. Notes: 1U = 1000 cm3. Radiation tolerance of electronics must be rated for mission lifetime.

or inverse sensitivity). As the observatory is at a distance D from the artificial star, the flux at the telescope is fC(λ) =FC(λ)/4πD

2, and the relationship is actually fC(λ) = R(λ) ×S. The calibration from the artificial star is then transferred to the celestial source via:

fsource = R(λ)× ssource. For a space-based observatory, R(λ) is the integrated response of all components in the light path, including the detector. It is different for each instrument and will change with time due to component aging, contamination, etc. Temporal changes are generally small, e.g. 0.1% per year (e.g. HST WFC3) and are wavelength dependent. For a ground-based telescope observing a space-borne artificial star, the terrestrial atmosphere is an additional complicating component of R(λ) due its variability on many time scales.

This can be addressed with multiple observations of many standard stars over a range of airmass, if obtained using a telescope at a high-quality site. For example, Mann et al. (2011) demonstrated 0.1% photometry from Maunakea.

Space-borne artificial star A critical issue in producing accurate flux calibration is systematic effects; adding the requirement for sub-percent uncertainties demands stringent control of these sources of uncertainty. A robust solution needs different methods to guard against being influenced by a common systematic, as an initial study (Peretz, 2021) con-cluded. A single payload with multiple instruments enables robust cross-checking over re-liance on any single approach, however, each instrument must be able to provide the required accuracy. Efficiency leads to requirements for a space-borne calibration instrument (Table

1) that could be carried independently on a dedicated platform such as an orbiting satellite, e.g. Orbiting Configurable Artificial Star (ORCAS, Peretz (2021)), by a star shade at L2, or another independent platform to enable accurate end-to-end throughput vs. wavelength calibration throughout the operational lifetime of an observatory. Once calibrated, the ob-servatory is enabled to carry out astrophysical programs whose science objectives demand

Figure 3: This proposal is the first step - building an engineering demonstation unit (prototype) - towards the goal of placing a CANDLE in space. A prototype (EDU) allows us to develop the thermal, structural and optical models to design the engineering test unit in the next phase.

high accuracy and/or high precision observations. One specific and immediate application is establishing SI-traceable standard stars beyond the current limited set.

1.1.1 Impact and Relevance to NASA

Although the CANDLE is motivated by the need for accurate flux calibration for dark en-ergy measurements, CANDLE supports the Astro 2020 Decadal Survey’s science goals more broadly:

Cosmic Ecosystems Stellar demographics, Fundamental stellar parame-ters

Worlds and Suns in Context

Planet properties and planetary diversity, Habitable environments, Properties of exoplanet host stars

New Messengers and New Physics

Properties of dark matter and the dark sector, Physics of cosmic expansion and evolution of the universe

Laboratory Astrophysics, Data Archiving, Curation and Pipelines

1.2 CANDLE Engineering Demonstration Unit

We propose, as a first step towards developing a flight-ready calibration pay-load, to design, build and calibrate a prototype (engineering demonstration unit, EDU) artificial star: the CANDLE (Calibration using an Artificial star with NIST-traceable Distribution of Luminous Energy). The EDU will consist of at least two components: a single mode fiber (SMF) laser projector and a solar reflector. A third component is a programmable spectrum (PS) projector. The latter is a novel application of a spectral light modulator.

Figure 4: Schematic layout of the CANDLE. The positions of components for each mode are fixed and located within a baffle (grey, almost spherical structure). The baffle rotates about an axis (perpendicular to the page) to expose the output port for Laser mode (lower right) or programmable spectrum mode (lower left) and to align the convex mirrror for solar mode (top). Lasers are blue rectangles, their output fibers are the yellow lines. PS mode components are a collecting mirror (purple) 2 collimating mirrors (yellow), two Féry prisms (red), and the final mirror (yellow). The monitor detector unit (dark grey rectangle) can be placed at the output ports to measure the emitted light by rotating the baffle.

1.2.1 Engineering Demonstration Unit

A conceptual design is shown in Figure 4, wherein a diffuse black spherical baffle B rotates about the sphere center to select one of the operating modes. The simplest instrument is Solar Observing Mode, where a convex mirror mounted on the outside of B reflects the solar disk as a point source towards the telescope. In Laser Mode, bare fiber ends of the single mode fiber lasers line up with the output ports, directing light towards the telescope.

In Programmable Spectrum Mode the solar flux is collimated and focused onto a spectral light modulator before being directed to the output port, and thence the telescope. The PS instrument consists of an input collimator, two Féry prisms, a digital micromirror device (DMD) and an output collimator. The detectors and electronics are sufficiently compact to allow for a payload with several calibration systems, allowing for inter-comparison over the mission lifetime. This strategy also enables constraining systematic effects in any one system.

1.2.2 Output Monitor Detector

The different levels to which NIST can calibrate each type of device, and the different response timescales makes it essential to include two types of monitoring detctors – a pho-todiode and an electrical subsitution radiometer. The detector system (dark grey rectangle in Fig. 4), is placed at the output port to measure the emitted light providing the ref-erence response, and is sensitive to the entire wavelength range of interest. Silicon (for λ < 1000 nm), InGaAs (800 nm < λ < 1550 nm) and extended InGaAs or HgCdTe (1600 nm < λ < 2500 nm) photodiodes and electrical substitution radiometer (ESR) are packaged within the detector module. The ESR has flight heritage (Compact Solar Irra-diance Monitor, Richard et al. (2019)) and has a stable, spectrally-flat response over the wavelength range of interest, albeit a slower response than the semiconductor photodiodes.

1.2.3 Laser Mode

While a minimum of three wavelengths are required, four allows extending the wavelength range longward of 2μm, roughly matching the Roman Space Telescope range. Four single mode fiber lasers illuminate the output ports. Each laser is centered at a different wavelength, e.g., 530 nm, 880 nm, 1550 nm, 2200 nm, and has output power of ≤ 1 Watt. When possible, the selected lasers will have During operations, the CANDLE electronics record, digitize, timestamp and transmit the monitor detector response to the observatory. Then the monitor detector slides away from the output port and the observatory records the laser CANDLE light.

Variations in the laser emission are corrected by ratioing the background-subtracted observatory response to the monitor detectors’ response

1.2.4 Solar Mode

The sun’s spectral irradiance between 400 nm and 2500 nm is known to better than 0.3% (Richard et al., 2020; Coddington et al., 2021) and is stable to 0.1% irrespective of solar cycle phase. NASA missions have continuously monitored the solar energy output, the newest being TSIS-1 (Total and Spectral Solar Irradiance Sensor), launched in 2017 The Sun’s irradiance, Es(λ), at the CANDLE position can be determined precisely. In Solar Mode (Fig. 3d), the convex mirror M1 is rotated where it is illuminated by the Sun. M1’s radius of curvature M1 is a function of the diameter of the mirror base, DM1, and the observatory field of regard, FoR = 4θM , where θM is the acceptance angle, namely, RM1 = DM1/(2 sin θM .)

M1’s surface reflectance, ρM1(λ) is designed for maximum reflectance, zero transmittance, and minimum spatial, spectral and temporal variation. The telescope, at a distance ro, will see the CANDLE reflected Sun (as a point source) if it is within the field of regard, and per Schiller (2012), the reflected spectral irradiance to the observatory, Eo(λ), for the input solar spectral irradiance, Es(λ), is

E0(λ) = 1/4(RM1/ro) 2ρM1(λ)Es(λ) (1)

The time-of-night availability range is set by the maximum value of observatory-CANDLE- Sun angle for a fixed orientation of M1.

During actual flight operation, CANDLE’s position and orientation relative to the Earth and to the Sun needs to be accurately known to determine that the observatory is within the FoR and to know E0(λ).

During operations in Solar Mode, The observatory records its response to the CANDLE with M1 in place as shown in Fig.4. Solar glint reflections, lunar glints and Earth glints from the spacecraft all contribute to the background flux, which is measured with M1 rotated out of the way, and the baffle B in place.

1.2.5 Programmable Spectrum Mode

This mode enables several options using solar light to provide spectral illumination via a spatial light modulator (SLM) that could be digital micromirror device, a microshutter array, or a liquid crystal on silicon display. It is a key component for this mode, where (Fig. 4 top) solar light is collected and focussed by the solar irradiance collector, M0, onto the entrance slit, S1, of a double-subtractive spectrograph that has a DMD at an intermediate focus between two Féry Prisms, P1 and P2. Wavelength-tunable monochromatic light or broad band spectra can be provided by this mode, as shown in Fig. 5.

(a)

(b)

Figure 5: Image display on a Spatial Light Modulator, (a) digital micromirror device (DMD) by monochromatic light, (b) broad band programmable spectral energy distri-bution

In our current design, M0 extends beyond the 12U volume. As part of the project, we will ex-plore options for tucking M0 against the Baffle dur-ing launch, and unfolding it once in orbit anal-ogous to solar panel deployments.The mechanism that moves M0 one of three baseline mechanisms required for the CANDLE, the first rotates the background baffle B to select between the CAN- DLE operating modes, and the second rotate P1 slightly to select different bands as described be-low.

1. Monochromatic SED The red rays traced in Fig. 4 (lower left) correspond to a single wavelength of light. Solar irradiance is collected by mirror M0, reflected to M2 which illumi-nates a rectangular slit S1 in a light-efficient manner.

Slit S1 forms the entrance slit of a monochromator where the rays reflect from M3 and are dispersed and focused by Féry prism P1 onto the DMD. The spec-tral dispersion direction is in the long direction of the SLM (along its rows), so the set of rays drawn in Fig4 appears to illuminate only one DMD column since the ray trace is for a single wavelength. When only one column of pixels is on, the DMD acts as the exit slit of the monochromator. In this case the rays reflecting from this column of the SLM continue to Féry prism P2 and are re-collimated since P2 is oriented in the opposite direction from P1. Ideally P2 “undoes” the spectral dispersion of P1, as in any double-subtractive spectrometer. The collimated monochromatic beam is then projected the monochromatic beam to the telescope . By selecting different columns of the SLM, different wavelengths are selected. The telescope spectral response is measured by scanning through the DMD columns, one column at a time (Fig. 5a,) and subtracting the corresponding CANDLE background-subtracted image. The normalization is provided by the monitor detector.

2. Broadband Programmable SED By turning on the desired number of pixels in more than one column, the DMD enables shaping the incoming solar spectrum to output a desired SED.

This is the same process used in the spectral engine of the NIST Hyperspectral Image Projector (HIP) (Rice et al., 2006, 2012) and in commercial spectral light engines (MacK-innon et al., 2005). During pre-flight calibration a set of programmed, output SEDs can be made through an iterative process using a spectrometer in the output beam as described in (Rice et al., 2006) and shown in Fig. 5. An instrument calibration model will be developed to relate the DMD images for desired SEDs projected on orbit to those determined by iterative matching pre-flight, and appropriate corrections can be made.

3. Alternative PS Mode using an Integrating Sphere A major concern with the design of PS mode shown in Fig. 4 is how well the dispersed beam is undispersed by P2. An alternate design of the CANDLE in PS mode that largely mitigates this concern at the expense of overall efficiency is to replace P2 with Mirror M4 and focuses the spectrally-dispersed beam diffracted from a given order of the DMD into a small integrating sphere (IS), where it is spatially mixed and emerges as a spectrally/spatially homogenous source at the IS exit port.

Then the collimator comprised of M5 and M6 projects this beam to the observatory telescope just as in Fig.4lower left. The output source is monitored by a multi-mode fiber (F) that brings a sample of the integrated light from the IS to the monitor detector.

Diffraction Order

(2/3)λB λB

(nm) (3/2)λB

1 2623 3934 5902 2 1311 1967 2951 3 874 1311 1967 4 656 984 1475 5 525 787 1180 6 437 656 984 7 375 562 843 8 328 492 738 9 291 437 656 10 262 393 590 11 238 358 537 12 219 328 492 13 202 303 454

Table 2: Diffraction orders for a TI DMD in the visible and infrared.

DMD Diffraction If a DMD is used as the SLM, diffraction needs to be considered. A sim-ple model was developed and tested to under-stand DMD diffraction effects. In this model the DMD is regarded as a blazed diffraction grating, and the model agrees well with the experiment (Table 2 and Fig. 5) (Rice et al., 2009) The dif-ferent diffraction orders listed in Table 2 corre-spond to different angles of reflection from the DMD, and this has to be considered strongly for the design of PS mode, where only one diffrac-tion order at a time would be undispersed by P2.

The spectral range is divided into sub-ranges de-fined by the DMD diffraction order, and P1 is rotated such that the dispersed image from only a single sub-range at a time fits onto the DMD

– corresponding to the DMD diffraction order of maximum efficiency for that subrange. Qualita-tively, this is implemented by making slight ro-tations of P1, and potentially P2 and the DMD (SLM). In the interest of minimizing mechanisms, the design with the IS (Fig.4) would only require rotation of P1 and the DMD, which would require a third CANDLE mechanism.

For example, when using the CANDLE for Roman calibration in filter band F129, centered about 1290 nm and a few hundred nm wide, the maximum efficiency angles corresponding to DMD order 3 would be chosen. Similarly, DMD order 4 corresponds roughly to Roman band F106, centered near 1060 nm, and DMD order 2 corresponds roughly to Roman band F184, centered near 1840 nm. For other Roman bands the nearest DMD diffraction order would be chosen. For example, for Roman band F158, centered near 1580 nm, DMD order 2 would be used, albeit at lower DMD efficiency.

Background Subtraction When the CANDLE is in orbit, the observatory detects the CANDLE’s emitted light plus a background, that includes, depending on the specific orbit, reflections from ”shiny” surfaces on the CANDLE carrier, solar glints, lunar glints, zodiacal light, etc. Subtraction of the background is accomplished by closing the output ports e.g.,by sliding the baffle, acquiring an image without the emitted light, ’the background image’, which is then removed from the illuminated observation. Thus the true Flux = (Signal + Background) - Background. This procedure applies to all CANDLE modes. For solar mode, the baffle is rotated, moving the convex mirror out of the observatory line of sight.

Flux estimates. Table ?? gives flux estimates for a CANDLE payload in an earth-orbiting satellite whose apogee is approximately 2× 108 km.

1.3 CANDLE EDU characterization

CANDLE’s in-flight spectral irradiance, Eo(λ) in Laser Mode or PS Mode will be known from a combination of pre-flight calibration, on-board monitoring, and robust theory. For this proposed program the CANDLE prototype’s exiting light will be calibrated at NIST using one or more of the NIST-traceable reference detectors with known absolute irradiance responsivity, such as those in routine use at the NIST SIRCUS facility (Brown et al., 2006;

Woodward et al., 2018). The CANDLE’s Silicon, InGaAs and ESR monitor detectors will be calibrated individually at NIST’s Spectral Comparator Facility (SCF) and/or the SIRCUS facility. SCF covers the wavelength range between 200nm and 1800nm and SIRCUS covers the range from 200nm to 5000nm.

1.3.1 Calibration of output irradiance

The procedure for calibrating either the Laser and PS CANDLE modes is to first align the optical axis of a CANDLE output port to a well-defined orthogonal reference plane. Next, a NIST reference detector is placed at the plane, illuminated by a CANDLE mode and the detected signal recorded. Background response is acquired by turning off the CANDLE light and recording the ”dark” signal. This step is repeated with the CANDLE monitor detectors (which are affixed to the inside of the CANDLE Baffle). The ratio of NIST reference detector signal to CANDLE monitor detector signal provides the relative calibration. Applying the absolute responsivity calibration factor of the NIST reference detector to this ratio calibrates the CANDLE light mode/monitor pair such that the monitor detector response subsequently indicates the absolute spectral irradiance at that particular external output. As an example, to calibrate a single mode fiber laser at 1550 nm, a NIST HgCdTe reference detector is used in combination with the InGaAs and/or HgCdTe CANDLE monitor detector.

In PS Mode, the light source is the sun, but in the laboratory we will require a solar simulacrum to provide the input beam. Part of the design activities is to construct a suitable solar simulator. The particular choice of input light source, as long as it provides sufficient flux and stability, does not affect the PS mode calibration, though stray and diffraction must be considered properly and accounted for in the error budget. It is the spectral irradiance of the output beam relative to the signal measured by the monitor detectors – not the absolute input flux – that is calibrated. Otherwise, the calibration procedure is the same as for Laser Mode.

1.3.2 Beam Profile Measurements

The CANDLE Laser Mode irradiance is calibrated in a laboratory, where the reference plane is within a few meters of the output port. For astronomical observatory calibration, the ref-erence plane (i.e., the telescope) is thousands (104 to 108) of kilometers away. Hence the need for applying a robust theory of flux propagation and additional laboratory measurements.

A single mode fiber with an ideally cleaved and polished bare output port has a far-field flux profile that is theoretically Gaussian and propagates as 1/r2. For the CANDLE’s single mode fiber diameters, the output laser beam reaches the far field at r > 0.1 m.

To the extent that it can be verified that a SMF has a Gaussian profile at rlab > 0.1m, the profile at the observatory distance, ro, can be predicted from far-field theory and the absolute spectral irradiance calibration at the rlab reference plane propagated to the ro reference plane.

Laboratory profile measurements made over a range of distances will verify the profile and 1/r2 fall-off. The uncertainty in the parameter fits of the theory to the laboratory (and/or on-orbit) data can then be propagated to the uncertainty of the irradiance at ro.

Several techniques for profiling and characterization of the beam are :

1. At short propagation distances, a camera with a 2-D pixel array will be used to directly profile the beam where the beam reasonably fits in the area defined by the sensor array

2. At larger propagation distances, three options are considered.

a) Raster scan the beam using a small area photodiode.

b) Raster scan the beam using the 2-D camera.

c) Illuminate a large target (e.g., a sheet of polytetrafluoroethylene, PTFE) with the source beam and image it with the camera equipped with an appropriate lens.

In each case, the beam profile measurements are obtained at a range of distances to determine divergence and stability of the profile with beam propagation. Measurements at short propagation distances can be done using an optical rail system or an automated z-axis stage up to several meters whereas larger propagation distances ranging from 10 meters to 100 meters can be made utilizing NIST’s telescope calibration facility1. These techniques will be evaluated, assessed for uncertainty, and compared to theoretical models. The best will be used to measure the properties of an actual CANDLE payload.

1(https://www.nist.gov/laboratories/tools-instruments/telescope-calibration-facility-tcf)

Early Results from Lab Tests of Laser Beam Profiles Preliminary measurements of the far-field beam profile for a single-mode fiber laser using a monochrome USB camera (2048× 1088 pixels) have begun. Figure 6 shows the beam profile emitted from a single-mode fiber laser at 638.5 nm measured by the camera at two distances along an optical rail. Panel a) shows the images (left) and 3D surface plots (right) of the beam profile at approximately 1.1 inches (top) and 3.9 inches (bottom) propagation dis-tance as the average of 10 images collected at 0.2 ms and 4 ms exposure times, respectively.

Panel b) shows the x-profile through the centroid of each beam along with a fit of a 1D Gaus-sian function to the pixel intensity data. These initial images show a smooth beam profile that is well represented by a Gaussian function except for a slight deviation in the wings as seen in the 1.1 inch distance profile at around 600 pixels and 1500 pixels number. These initial images show a smooth beam profile that is well represented by a Gaussian function except for a slight deviation in the wings as seen in the 1.1 inch distance profile at around 600 pixels and 1500 pixels number. At the larger, 3.9 inch propagation distance, the beam is expanded and gives a nearly flat profile across the center 100 pixels of the beam but with pixel-to-pixel variation of around 0.8%. For a 10 m telescope on the ground, the portion of the beam sampled will be less than a single pixel from what is represented in the beam pro-files shown in Figure 6. Any non-ideal behavior in the beam generated at either the source or ground-based detector, i.e. due to a speck of dust on the optical fiber or laser speckle for example, will cause difficulties in the end calibration. The existing climate-controlled indoor optical testing range with a linear free optical path length of 80 m at NIST will aid in these upcoming tests.

Computational Electromagnetic Simulation of CANDLE Light Sources and Optics Careful comparisons of optical measurements made within the laboratory (and within out-door environments) with associated computational simulations of expected observations will be critical for the precision characterization and the detailed understanding of CANDLE optics. Computational simulations of optical systems are generally of one of two types: 1) Ray tracing, in which either photons, or groups of photons, are considered to be individual particles (referred to as “rays”) that do not interfere or interact at all with one another.

(Thus, ray tracing simulations can never simulate optical effects such as coherence, diffrac-tion, or interferometry at all.) 2) Non-ray-tracing optical electromagnetic simulations, which do tend to take the wave nature of light into account (at least to first order), however typ-ically at a larger cost in computational simulation speed when compared with simple ray tracing. Since full computational time-dependent analytic solutions to Maxwell’s equations are usually intractable, even non-ray-tracing optical electromagnetic simulations typically need to use some forms of computational approximations: a very commonly-used modern one is the so-called “finite difference time domain” (FDTD) method

In our simulations of CANDLE optics, we will be performing ray tracing using the open-source ROBAST package (https://robast.github.io) (in addition to ray trace modelling using closed-source packages, e.g. Zemax); and performing non-ray-tracing FDTD simula-tions using the open-source MEEP package (https://meep.readthedocs.io).

The detailed simulation of CANDLE optics, per the above, has just begun, and will provide a critical way of helping the team to precisely understand the output of CANDLE optical sources following construction, during both the testing and the operation phases of

Figure 6: a) Images and 3D surface plots of a beam emitted from a 638.5 nm single-mode fiber laser directly onto the CCD camera array at approximately 1.1 inches (top) and 3.9 inches propagation distance (bottom).

b) 1D profiles through the centroid of the beam (green line panel a) along with Gaussian fits to the pixel intensity data. These data show we have the basic capabilities required to make the necessary laboratory testing measurements.

the CANDLE engineering demonstration unit.

1.3.3 CANDLE Uncertainty Budget

A key result of this project will be to identify sources of measurement and systematic un-certainty, and investigate methods of reducing or minimizing their effect on the principal objective of reaching the target 0.4%.

Common to all modes are: table goes here when compiling works

1.4 Management Plan

1.4.1 Tasks and Timeline

We have identified 8 principal task groups, shown in Table 3. Some tasks may be carried out concurrently with others, e.g., Task 5 with 2 through 4 and Task 6 with 2 through 8.

EDU design, Task 1, must begin first chronologically, as the design and layout of the EDU will be determined at this stage, as will the component specifications needed for Task 2 – procurement. While components may be purchased in sequence, parts with long lead times will be identified during Task 1 so that these can be first “in the queue”. Certification of EDU components at GSFC is Task 3. Although our objective is to build and test a prototype CANDLE, when feasible we will use components that have or could have high TRL values.

For example, some of the lasers are at TRL 6 (fibertek, etc), similarly, the ESR has known flight heritage. As feasible, other components may be flight qualified at GSFC.

Exit beam profiling is the subject of Task 4, and Task 5 is to develop a programmable spectrum for calibration. Integration and testing of the EDU comprises Task 7 and calibra-tion of the EDU, Task 8. Task 6 develops possible operation modes for a CANDLE in, for example, low earth orbit, high earth orbit, an elliptical orbit with apogee at 200,000 km like the proposed ORCAS satellite (see Peretz (2021) and at a distance of 75,000 km from an L2