In-flight Performance and Calibration of the LOng Range Reconnaissance Imager (LORRI) for the New Horizons Mission

After the LORRI aperture door was opened on 2006 August 29, the CCD temperature has typically been within a few degrees of −81 °C. At this temperature, the CCD dark current is usually negligible for most LORRI observations. The process used to subtract the CCD electronic offset signal (which is called the "bias" level and is used to prevent sending negative analog signals to the analog-to-digital converter) automatically includes any dark current that may be present. From a series of long exposure time images (up to 64.967 s) taken during a test in 2019 July when the CCD temperature was −81 °C, we determined an upper limit for the dark current in 1 × 1 pixels of 0.0019 DN s⁻¹ pixel⁻¹, corresponding to 0.040 e s⁻¹ pixel⁻¹ at the nominal gain of 21 e pixel⁻¹, which is approximately 10 times larger than the dark current calculated using data from the CCD manufacturer's specification sheet. During long exposure (≥10 s) 4 × 4 images obtained during flight, "warm" pixels are clearly detected with elevated dark currents (up to a few DN in magnitude, after subtraction of the median bias plus dark level). The locations of these "warm" pixels vary over time, but they never comprise more than 1% of the total number of pixels in the image.

The bias level is a function of the temperature of the FPE board. From the ground calibration data, we derived that the bias level for 1 × 1 images is given by:

$$\begin{eqnarray}&&\mathrm{bias}=503.968\,(\pm 0.549)+1.239\,(\pm 0.015)\ast {T}_{\mathrm{board}}\end{eqnarray} \tag{ 1 }$$

where "bias" is the bias level in DN and T_board is the FPE board temperature. For 4 × 4 images the bias level is typically ~4 DN larger. LORRI in-flight images have bias levels that are generally consistent with this formula. After the LORRI aperture door was opened on 2006 August 29, the FPE board temperature has typically been in the range 23 °C–29 °C.

We have recently (in 2019) noticed that the bias level may also display a "start-up" feature, whereby the bias level starts at a slightly higher value and gradually plateaus to its expected value over the course of several minutes. This behavior is still being characterized, but the magnitude of the effect is at the sub-DN level, which is inconsequential for most New Horizons science applications. We do, however, want to understand this effect better because it will likely affect LORRI's ability to accurately measure the extragalactic background light (Zemcov et al. 2017).

As implemented in the LORRI pipeline, the bias+dark subtraction is a two-step process. First, the overall bias+dark level for an image is subtracted from the raw ("Level 1") image. Specifically, for 1 × 1 images (i.e., Level 1 files having 1028 × 1024 pixels) the median intensity of the pixels in columns 1024−1027 of the Level 1 image (corresponding to columns 1032−1035 of the CCD, which are in a portion of the CCD not directly illuminated) is subtracted from each pixel in the Level 1 image. For 4 × 4 images (i.e., Level 1 files having 257 × 256 pixels), the median intensity of pixels in column 257 (which is the re-binned version of CCD columns 1032–1035 in the 1 × 1 image) is subtracted from each pixel in the Level 1 image. Since the bias columns also accumulate CCD dark current, the median dark current is also removed during this step.

The simple median of the pixels in the inactive region may not provide the best estimate of the global bias+dark level, if the distribution of pixel values is distorted by multiple cosmic rays, or other artifacts. We have recently investigated an alternative approach, using fits to the well-defined peak in the histogram of the pixel values as the bias level estimate. Although this technique may indeed provide a better estimate of the true bias level, we have found that the differences with the median values are typically ≤0.3 DN, which is smaller than the typical electronics noise level (~1.1 DN). We have decided to stick with the simple median for the near-term because this approach is more robust (i.e., not subject to subtle computational issues) and easier to implement. However, we may eventually employ a different technique to enable achieving the highest possible sensitivity for the most demanding observations.

After this global bias+dark level is subtracted, a "delta-bias" (sometimes called a "superbias") image is then subtracted from the image. The delta-bias image captures the pixel-to-pixel variations in the bias and was created by averaging 100 1 × 1 bias frames (i.e., images with exposure times of 0 s) taken in-flight on 2006 July 30 with the main aperture door closed, as part of a LORRI in-flight calibration activity (Figure 8). The delta-bias image for 4 × 4 format images was obtained by simple re-binning of the average 1 × 1 delta-bias image. Although 4 × 4 bias images were obtained in 2006 April and May, those were contaminated by light passing through the small circular window (~2.54 cm in diameter) in the main aperture door. This window was placed in the aperture door to permit LORRI to have some imaging capability in case the main aperture door did not open. The light passing through this small window was too weak to affect the 1 × 1 bias images, but could be faintly seen in the 4 × 4 bias images.

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Bias images in both 1 × 1 and 4 × 4 format have been taken at least once per year during the entire New Horizons mission. No systematic change in the bias images has ever been seen. LORRI images (both bias images and regular images) sometimes exhibit a small even–odd column signal offsets ("jail bars"), but the effect is generally ≤0.5 DN in magnitude, which is smaller than the typical electronics noise (~1.1 DN). We have not been able to correlate the appearance of the jail bars with any particular instrument parameter (e.g., there is no correlation with the temperatures of the CCD or the electronics). But if they are present, the jail bars are usually present in an entire set of images taken near the same time. In that case, the jail bars can be removed fairly easily with standard image processing techniques (e.g., by creating a template image with the jail bar pattern and subtracting that from the original image).

Individual LORRI images in both formats also display a low-level (≤1 DN) horizontal (i.e., row-based) pattern that is apparently associated with the injection of non-random noise during the CCD frame transfer process. This "horizontal striping" is always present but is usually only evident when large portions of the image have little or no signal (e.g., when observing sparse star fields). The stripes change locations from frame-to-frame producing a non-random noise pattern across each image. This pattern can be removed from an individual image with standard image processing techniques (e.g., by subtracting a median smoothed, or robust average, level from each row).

The electronics noise is measured by subtracting one bias frame from another and examining the residuals. This technique has been applied throughout the mission, and the results demonstrate that the electronics noise has remained virtually the same for the entire mission (~1.1 DN) for both CCD formats.

As already mentioned above, LORRI does not have a shutter. Thus, the target being observed illuminates the active region of the CCD whenever LORRI is pointed at the scene. In particular, the CCD continues to record the scene as the "scrub" is performed (before the nominal start of the exposure) and as charge is transferred from the active portion to the storage area (after the nominal end of the exposure). Both of these processes result in a smearing of the observed scene along a CCD column.

The smear process can be visualized as pulling a sheet of light sensitive film, whose size is exactly the size of the CCD's active area, uniformly across a scene whose size is also exactly the size of the CCD's sensitive area. The flush begins as the film is pulled across the scene starting from the top of the CCD (i.e., starting at the highest CCD row) until the film exactly covers the full scene. The total flush time is the duration of that process, and the rate of motion, which is also the row transfer time, determines how much signal from pixels at higher rows is transferred to any particular pixel in the same column. After the flush process is completed, the film stays in place for the commanded exposure time, and each pixel accumulates signal only from the scene imaged at that pixel. After the exposure is completed, the film is pulled in the same direction as before, but this time each pixel will accumulate signal from the scene in rows below that pixel as the film is moved to the image storage region of the CCD, which is also completely outside the illuminated scene. The total transfer time is the duration of that process, and the rate of rate of motion during the transfer determines how much signal from pixels at lower rows is transferred to any particular pixel in the same column. All of the pixels in the CCD storage region are then transferred row-by-row to the CCD serial readout register, where the analog signals are amplified and then digitized.

For images with no over-exposed pixels and that have fixed pointing during the exposure, the smear can be essentially completely removed using the algorithm described in Cheng et al. (2008). Once a pixel is over-exposed, however, information on its true intrinsic level is lost and the smear correction will be incomplete for that column of the image. As the de-smear algorithm works on a column by column basis, any significant motion of the camera during the exposure in the row direction (i.e., perpendicular to the columns), as can occur when LORRI is used in ride-along mode with the New Horizons MVIC or LEISA instruments, may also limit the accuracy of the correction. Of course, the de-smear correction cannot remove the extra shot-noise associated with the smeared light. For long exposures this is only a modest effect, but for images of extended targets with short exposure times (i.e., similar to, or smaller than, the total frame transfer time of ~12 ms), the signals generated during the scrub and transfer processes are comparable to, or even larger than, the signal levels accumulated during the nominal exposure time. In this case, the shot noise from the smear signal produces significant degradation of the S/N. For example, when the signal accumulated during the exposure time is comparable to that accumulated during the scrub and transfer, the S/N is reduced by approximately $\sqrt{2}$ compared to the case when frame transfer smear is negligible.

The de-smear algorithm described in Cheng et al. (2008) is complex and computationally intensive. Given the sparse nature of the "error matrix" used in that formulation, we identified a technique for speeding up the calculations by a factor of ~10 compared to performing the matrix multiplications given in Cheng et al. (2008). This faster technique, which produces results essentially identical to those using the full matrix multiplication, has been used in the LORRI data pipeline since 2014.

We have recently investigated two alternative formulations for the desmear step, which are simpler and easier to implement than the algorithm given in Cheng et al. (2008). One of the algorithms (Owen et al. 2019, in press) adopts approximations to accelerate the computation by avoiding matrix operations. Another algorithm, discussed further below, is exact but involves a matrix inversion for each image. The new algorithms are still being evaluated and must be tested extensively before either can be used in the LORRI calibration pipeline.

2.2.1. An Exact Simple De-smear Algorithm

We are presently investigating an alternative algorithm for the de-smear step, which is simpler and easier to implement than the algorithm given in Cheng et al. (2008). As with the Cheng et al. (2008) approach, the new algorithm is applied on a per column basis, since the smeared charge associated with any pixel stays within its column. The solution is derived with a single matrix multiplication that transforms the column of data values as generated by LORRI to a column of pixel values corrected for charge-transfer smear.

For any column of pixels in the LORRI CCD, neglecting dark current, the rate at which signal is accumulated in a LORRI CCD pixel within that column can be written as:

$$\begin{eqnarray}&&\displaystyle \frac{{S}_{k}}{{t}_{\exp }}=\sum _{i,i\gt k}^{n}{R}_{i}\,{I}_{i}\,\displaystyle \frac{{t}_{\mathrm{scrub}}}{{t}_{\exp }}+\sum _{i,i\lt k}^{n}{R}_{i}\,{I}_{i}\,\displaystyle \frac{{t}_{\mathrm{transfer}}}{{t}_{\exp }}+{R}_{k}\,{I}_{k}\end{eqnarray} \tag{ 2 }$$

where:

• S_k is the measured signal in a pixel in row k (electrons, or "e").
• R_x is the intrinsic responsivity of pixel x ((e s⁻¹ pixel⁻¹)/(photons s⁻¹ pixel⁻¹)).
• I_x is the input photon flux at pixel x (photons s⁻¹ pixel⁻¹).
• t_exp is the total exposure time (s), which is the commanded time plus 0.6 ms.
• t_scrub is the CCD row transfer time during the frame scrub (s).
• t_transfer is the CCD row transfer time during the frame transfer (s).
• n is the number of rows in the image (1024 for 1 × 1 images and 256 for 4 × 4 images).

The first term on the right-hand side of the equation represents the smear contribution to the observed signal from pixels in the same column, but at larger row numbers compared to the pixel of interest, and is accumulated during the frame scrub process. The second term on the right-hand side of the equation represents the smear contribution to the observed signal from pixels in the same column, but at smaller row numbers compared to the pixel of interest, and is accumulated during the frame transfer process. The third term is the actual desired quantity, the signal accumulated at the pixel of interest during the commanded exposure time.

Equation (2) can be recast as a matrix equation:

$$\begin{eqnarray}&&{D}_{i}=\sum _{j=1}^{n}{g}_{{ij}}\,{F}_{j}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\to {\boldsymbol{D}}={\boldsymbol{G}}\,{\boldsymbol{F}}\end{eqnarray} \tag{ 4 }$$

where in any CCD column:

• D_i is the detected signal (including smear) at row i (DN).
• F_j is the true signal (not including smear) at row j (DN).
• g_ij are coefficients determined as described below.

The coefficients of ${\boldsymbol{G}}$ are analogous to, but not identical to, the coefficients in the smear formulation of Cheng et al. (2008). For LORRI, the frame scrub takes a total of 12.15 ms, which means each row transfer (t_scrub above) takes 0.0119 ms for 1 × 1 images and 0.0474 ms for 4 × 4 images. The frame transfer takes 11.12 ms, which means each row transfer (t_transfer above) takes 0.0109 ms for 1 × 1 images and 0.0434 ms for 4 × 4 images. Note that ${g}_{{ij}}=1$ when $j=i$, ${g}_{{ij}}={t}_{\mathrm{scrub}}/{t}_{\exp }$when $j\gt i$, and ${g}_{{ij}}={t}_{\mathrm{transfer}}/{t}_{\exp }$ when $j\lt i$.

In summary, the measured count rates for the pixels in a column (represented by the column matrix ${\boldsymbol{D}}$) can be represented by the matrix multiplication of the smear matrix and a column matrix of the actual count rates (i.e., ${\boldsymbol{F}}$, the count rates after the smear contributions have been removed). Thus, the desmear problem reduces to finding the inverse of the smear matrix:

$$\begin{eqnarray}&&{\boldsymbol{F}}={{\boldsymbol{G}}}^{-1}\,{\boldsymbol{D}}.\end{eqnarray} \tag{ 5 }$$

Note that the matrix inversion need only be performed once for each image because the smear matrix is identical for each column in the image. In fact, the smear matrix depends only on the ratios ${t}_{\mathrm{scrub}}/{t}_{\exp }$ and ${t}_{\mathrm{transfer}}/{t}_{\exp }$. In principle, the matrix inversion could be performed in advance for each exposure time employed, in which case the matrix inversion within the calibration pipeline could be replaced by a simple lookup of the appropriate inverted matrix, which could be stored in a reference file directory (e.g., similar to what is done for the delta-bias and flat field).

Flat-fielding refers to the process of removing the pixel-to-pixel sensitivity variations in the image. An exposure obtained by illuminating the LORRI aperture uniformly with light is called a flat-field image. During ground calibration testing, flat-fields were obtained by using an integrating sphere to provide uniform illumination (Morgan et al. 2005). The light source was a xenon arc lamp with a spectrum similar to that of the Sun. The absolute intensity of the input illumination was measured using a calibrated photodiode. For the panchromatic case, which is the one most relevant for flat-fielding LORRI images, the light from the xenon lamp was unfiltered. Flat-field images were also obtained by passing the light through bandpass filters centered at five different wavelengths spanning the range over which LORRI is sensitive, prior to injection into the reference sphere, to estimate the sensitivity of the flat-fields to the spectral distribution of the source. The spatial patterns in the flat-field images change significantly with wavelength. However, the variation in panchromatic flat-fields caused by differences in the spectral distribution of the illumination source are much less significant. Indeed, panchromatic flat-field images produced using a tungsten lamp were virtually indistinguishable from those produced by the xenon lamp. Flat-fields were obtained at four different sets of thermal environments (at standard laboratory room temperature, and at the lowest, nominal, and highest temperatures predicted for in-flight conditions), but no significant variations in the flat-field images were detected.

No suitable flat field astronomical target was available after launch. The flat-field reference file used in the LORRI calibration pipeline was produced by averaging 100 flat-field images taken at room temperature during ground testing using the xenon arc lamp as the light source, debiasing and desmearing the average image as described earlier, and normalizing the intensities in the active region to a median value of 1 (Figure 9). If S (units are DN) is an image of a target that has already been desmeared and debiased, and if FF is the reference flat-field image, then the flat-fielded (i.e., photometrically corrected) target image (C; units are DN) is given by C = S/FF.

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The LORRI flat-field has been monitored throughout the New Horizons mission by taking exposures with onboard "cal lamps," which refer to two small tungsten filament lamps mounted on opposite sides of the CCD, in close proximity to the CCD. The primary function of these onboard lamps is to provide illumination of the CCD during "functional" tests, which verify basic operation of the CCD and its electronics, but not the OTA. The illumination provided by the lamps is highly non-uniform spatially (see the top row of Figure 10) but is highly stable over time. The temporal stability of the lamps has been monitored annually throughout the mission. Ratios of lamp images taken at different times provide a sensitive measure of the stability of the lamps (see the bottom row of Figure 10). The histogram for the lamp #2 ratio image in Figure 10 is a bit tighter than the histogram for the lamp #1 ratio image, but both lamps show remarkable temporal stability with the average, median, and most common ratio values within 0.1% of unity for both lamps. Furthermore, these lamp images demonstrate that he particles on the CCD have not moved over the entire duration of the mission (i.e., their locations are fixed in CCD coordinates), which means the flat-field correction employed by the calibration pipeline accurately removes any artifacts they might create during observations.

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The software pipeline that performs the calibration steps defined above does not perform the conversion from DN to physical units because that conversion requires knowledge of the SED of the target. (The SED is related to the "color" of the target in standard astronomical usage.) Instead, various LORRI FITS header keywords ("photometry" keywords) are provided that allow users to convert from DN to physical units depending on the spectral type and spatial distribution (diffuse versus point source) of the target. Photometry keywords are provided for targets having spectral distributions similar to Pluto, Charon, Pholus, Jupiter, MU69, and the Sun. The units adopted for the radiance (also called "intensity") of diffuse targets are erg cm⁻² s⁻¹ Å⁻¹ sr⁻¹ . The units adopted for the irradiance (also called "flux") of point (i.e., unresolved) targets are erg cm⁻² s⁻¹ Å⁻¹. The latest (i.e., current) values of the photometry keywords are provided in the header of the calibrated (called "Level 2") FITS file for the image being analyzed. The photometry keywords derived from the in-flight calibration campaign conducted in 2016 July, using the star HD 37962 (with a solar-type SED) as the absolute calibration standard, is provided in Table 2. All of these keywords enable conversion of raw signals in engineering units to absolute signals at the so-called "pivot" wavelength (λ_pivot), which is one way of characterizing the "effective" wavelength for a broadband optical instrument. The pivot wavelength is defined as:

$$\begin{eqnarray}&&{\lambda }_{\mathrm{pivot}}=\sqrt{\displaystyle \frac{\int \mathrm{QE}\ast \lambda \ d\lambda }{\int \mathrm{QE}/\lambda \ d\lambda }}\end{eqnarray} \tag{ 6 }$$

where "QE" is the total system quantum efficiency (see the next section). The pivot wavelength for LORRI is calculated to be 6076 Å.

For convenience to users, we provide a prescription for converting LORRI signal rates to standard V magnitudes in the Johnson photometric system:

$$\begin{eqnarray}&&V=-2.5\mathrm{log}(S/{t}_{\exp })+\mathrm{ZPT}+\mathrm{CC}-\mathrm{AC}\end{eqnarray} \tag{ 7 }$$

where V is the magnitude in the standard Johnson V band (i.e., specifies the target's flux at 5500 Å), S is the measured signal in the selected photometric aperture (DN), t_exp is the exposure time (s), ZPT is the photometric zero-point (18.78 for 1 × 1 and 18.88 for 4 × 4), CC is a color correction term (as specified in Table 3), and AC is an aperture correction term to convert from the flux collected in a specified synthetic aperture to the total flux integrated over the LORRI PSF. The CC terms listed in Table 3 were calculated using SEDs for the listed spectral types. For the specified stellar types, we used SEDs downloaded from the exposure time calculators at the Space Telescope Science Institute. For the other listed spectral types, we used SEDs adopted by the New Horizons team, which are based on published spectra. For typical LORRI observations of point sources, the S/N is optimized by integrating over a circular aperture with a radius of 5 pixels (1 × 1 format) or 3 pixels (4 × 4 format), in which case AC is either 0.10 or 0.05, respectively.

We provide here two examples showing how to convert from engineering units to physical units: one for a diffuse target and one for a point (i.e., unresolved) target. Consider a diffuse target whose spectrum is similar to that of Pluto's globally averaged SED. In this case, the RPLUTO photometry keyword in the header of the Level 2 (i.e., calibrated) file should be used to convert from the observed count rate in a pixel to a radiance value at LORRI's pivot wavelength:

$$\begin{eqnarray}&&I=S/{t}_{\exp }/\mathrm{RPLUTO}\ (\mathrm{diffuse}\ \mathrm{target})\end{eqnarray} \tag{ 8 }$$

where:

• I is the diffuse target radiance (erg cm⁻² s⁻¹ Å⁻¹ sr⁻¹) at ${\lambda }_{\mathrm{pivot}}$.
• S is the measured signal in a pixel (DN).
• t_exp is the exposure time (s).
• RPLUTO is the LORRI diffuse photometry keyword for targets with Pluto-like SEDs.

Since the solar flux (F_☉) at a heliocentric distance of 1 au at the LORRI pivot wavelength is 176 erg cm⁻² s⁻¹ Å⁻¹, the value for the radiance can be converted to I/F (where $\pi F={F}_{\odot }$), which is a standard photometric quantity used in planetary science, using:

$$\begin{eqnarray}&&I/F=\pi {{Ir}}^{2}/{F}_{\odot }\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&\to I/F=(S/{t}_{\exp }/\mathrm{RPLUTO})\ast \pi {r}^{2}/{F}_{\odot }\end{eqnarray} \tag{ 10 }$$

where "r" is the target's heliocentric distance in astronomical units.

For unresolved targets (e.g., planetary targets observed at large ranges), the absolutely calibrated flux (also called the irradiance) at the LORRI pivot wavelength can be determined using the point source photometry keywords. For a target with an SED similar to that of MU69, the observed count rate integrated over the LORRI PSF can be related to the flux (not to be confused with "F" in "I/F") at the LORRI pivot wavelength by:

$$\begin{eqnarray}&&F={S}_{\mathrm{total}}/{t}_{\exp }/\mathrm{PMU}69\ (\mathrm{point}\ \mathrm{target})\end{eqnarray} \tag{ 11 }$$

where:

• F is the point target flux, or irradiance (erg cm⁻² s⁻¹ Å⁻¹).
• S_total is the total signal from the target integrated over the PSF (DN).
• t_exp is the exposure time (s).
• PMU69 is the LORRI point source photometry keyword for targets with MU69-like SEDs.

When observing stars, it is more common to convert the absolute flux to a magnitude in a standard photometric system. For an A-type star observed by LORRI, the V magnitude is given by:

$$\begin{eqnarray}&&{V}_{\mathrm{star}}=-2.5\mathrm{log}({S}_{\mathrm{total}}/{t}_{\exp })+\mathrm{ZPT}-0.060\end{eqnarray} \tag{ 12 }$$

where V_star is the star's magnitude in the standard Johnson V band, S_total is the total signal integrated over the LORRI PSF (DN), t_exp is the exposure time (s), ZPT is the photometric zero-point (18.78 for 1 × 1 and 18.88 for 4 × 4), and the color correction term is −0.060.

LORRI's optical performance has been monitored throughout the mission by observing star clusters. Measurements of the two-dimensional spatial distributions of individual stars enable characterization of the LORRI PSF across the entire FOV. Photometry of the individual stars is performed to monitor LORRI's sensitivity, both across the FOV and as a function of time. By using clusters whose stars are cataloged in one or more astrometric surveys, LORRI's geometrical distortion can also be measured and monitored as a function of time.

The galactic open cluster Messier 7 (M7; alternate names are NGC 6475 and the Ptolemy cluster) was used for LORRI's optical performance calibrations from 2006 through 2013. In 2013, we switched to the galactic open cluster NGC 3532 (alternate names are the Wishing Well cluster, the Pincushion cluster, and the Football cluster), primarily because NGC 3532 has a higher density of stars (Figure 11), which allows better areal coverage over the full CCD and improved mapping of LORRI's geometrical distortion. We observed both clusters during ACO-7 in 2013 so that later observations of NGC 3532 (i.e., those taken after 2013) could be compared to earlier observations of M7 (i.e., those taken between 2006 and 2013), thereby enabling systematic monitoring of LORRI's performance over the entire mission.

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The optical design of LORRI has a small amount of pin-cushion distortion, which is clearly detected in measurements of the star clusters (Figure 12). However, LORRI achieved its design goal of keeping the geometrical distortion ≤0.3% over the entire FOV. Spot checks of the geometrical distortion at different times in the mission have not shown any significant differences (i.e., the various distortion parameters do not change by more than their measurement uncertainties, at the 2σ level). The LORRI geometrical distortion is described in detail in the SPICE instrument kernel for LORRI, which is archived at the Small Bodies Node (SBN) of the Planetary Data System (PDS). The geometrical distortion coefficients described within the Simple Image Polynomial (SIP) framework, which is commonly used in astronomy, are captured in the LORRI FITS header keywords. We note also that the archived LORRI FITS files employ World Coordinate System (WCS) keywords to enable accurate transformations between native LORRI [x, y] pixel locations and standard astronomical coordinates (e.g., [R.A., decl.]).

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High S/N PSFs for both 1 × 1 and 4 × 4 LORRI images are displayed in Figure 13. These were created by combining multiple images of single stars located near the center of the LORRI FOV, including images taken with different exposure times to expand the dynamic range of the composite (e.g., for 1 × 1 images, using 100 ms exposures to sample the PSF cores and using 400 ms exposures to sample the PSF wings). Three diffraction spikes produced by the three struts of the OTA are clearly visible. The PSFs are not completely symmetrical; there is excess flux extending from the peak pixel toward the lower right, which is presumably produced by a slight misalignment of the OTA. This asymmetry in the PSF has been present at the same level throughout the mission, indicating it is a stable feature, which enables accurate deconvolution techniques to be applied when attempting to maximize the spatial resolution of LORRI images.

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A technique for creating properly sampled (i.e., Nyquist sampled) PSFs is described in Lauer (1999) and has been applied to LORRI images when multiple, dithered exposures are available. A good example is the LORRI imaging of Pluto's satellite Kerberos, when four separate images could be combined to create a composite with significantly higher resolution than the individual images (Figure 14). Deconvolution can also be used to remove motion smear for LORRI images taken during scanning observations of the Ralph instrument (e.g., Figure 7).

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Both the shapes and intensities of the stars in the calibration fields are used to determine whether there has been any degradation in the optical performance over the course of the mission. For example, contamination (e.g., ice accumulation) anywhere along LORRI's optical path could manifest as a reduction in photometric sensitivity and/or a broadening of the PSF. We monitor the PSF shape by fitting two-dimensional Gaussians to the stellar images each time the calibration fields are observed. We monitor LORRI's sensitivity by comparing the signals for the same stars measured at multiple epochs.

Figure 15 shows the results of the Gaussian fits to the stars measured during the observations of NGC 3532 during the calibration campaign in 2016 July. By comparing the PSFs from stars falling in five different regions of the CCD, we show how the PSF varies across the LORRI FOV. The PSF behavior exhibited in this figure is typical of what has been observed throughout the mission. Figure 16 explicitly compares the LORRI PSFs measured on M7 stars over a 5 yr period (2008–2013); there is no significant variation in the shape of the PSF over this period.

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The Gaussian fits applied to the star cluster images employed a ±10 pixel region centered on each star's peak pixel, which includes both the core and a significant fraction of the wings of the spatial brightness distribution. Restricting the fit to the core only, which is a better measure of LORRI's spatial resolution, results in a narrower full width at half maximum (FWHM). For example, using the same Gaussian fitting routine on the 1 × 1 PSF displayed in Figure 13 gives (XFWHM, YFWHM) = (2.06, 2.65) pixels when a ±10 pixel region is fit, and (XFWHM, YFWHM) = (1.87, 2.47) pixels when a ±2 pixel region is fit. Thus, we see that the LORRI PSF is slightly undersampled (relative to Nyquist) in the X (row) direction.

Photometry of M7 stars over a 7 yr period (2006–2013) demonstrates that there has been no significant change in LORRI's sensitivity during this time (Figure 17). Photometry of NGC 3532 stars over a 4.5 yr period (2013 July–2017 December) also shows no significant change in LORRI's sensitivity during this period (Figure 18). Combining all these results, and taking into account that the stars being sampled did not necessarily have constant fluxes during the times of the LORRI measurements, we conclude that LORRI's sensitivity has remain essentially unchanged (at the level of ~1%) over the entire duration of the mission.

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Since the SEDs of virtually all solar system targets are produced by scattered sunlight, we searched for absolute standard stars that are solar analogs to calibrate LORRI. Fortunately, two solar-type standard stars with absolute fluxes measured to an accuracy of ~1% (1σ) by the Hubble Space Telescope (HST) have V magnitudes that are suitable for high S/N LORRI measurements, and they are also visible from the New Horizons spacecraft at reasonably large solar elongation angles for the entire mission.

HD 37962 has V = 7.85 and $B-V=0.65$, which is identical to the solar color. This star was observed by LORRI on 2016 July 14, as part of the special post-Pluto calibration campaign. The solar elongation angle was 56°, and the solar scattered light level was negligible in all images. We obtained 5 different 100 ms exposures in 1 × 1 format and 5 different 50 ms exposures in 4 × 4 format. The observed stellar signals had S/N ≥ 140 in all 10 images. We used aperture photometry and the gain values discussed previously to calculate the total fluxes in electrons s⁻¹. As shown in Figure 19, the measured fluxes for the 1 × 1 and 4 × 4 images are in excellent agreement.

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HD 205905 has V = 6.74 and B − V = 0.62, which is slightly bluer than solar color. This star was observed by LORRI on 2016 July 16, also as part of the special post-Pluto calibration campaign. We obtained 5 different 100 ms exposures in 1 × 1 format and 5 different 50 ms exposures in 4 × 4 format. The observed stellar signals had S/N ≥ 100 in all 10 images. The solar elongation angle was 144°, and the solar scattered light level was negligible in all images. The photometry results for HD 205905 are fully consistent with the results obtained from HD 37962.

Figure 20 shows a comparison of the stellar and solar spectra. Given the remarkably solar-like SED for HD 37962, we decided to use that star as the primary LORRI absolute calibration standard. Assuming that LORRI's relative responsivity (see the next section) as a function of wavelength was accurately measured during the ground calibration (Morgan et al. 2005), we adjusted the absolute scale of the responsivity curve using a single constant multiplicative factor to force the calculated signal from HD 37962 to match the observed signal. The calculated signal is the integral over all wavelengths of the product of the star's SED in absolute units and LORRI's responsivity curve. The new LORRI responsivity curve produced in this way is discussed in the next section. For targets having solar-type SEDs, the absolute accuracy of the values derived from LORRI data should be comparable to the accuracy of the HST measurements (i.e., ~1%, 1σ) because the LORRI calibration is tied to the absolute flux from HD 37962. However, the accuracy of the LORRI calibration also depends on the accuracy with which the total measured LORRI signal from HD 37962 is determined. The peak pixel during these measurements has S/N ≥ 100, but we use aperture photometry with a radius of 5 pixels (for 1 × 1 images; we used a 3 pixel radius aperture for 4 × 4 images) to measure the signal and then use the PSF described in Section 3.1 to correct to the signal for an infinite aperture (i.e., integrated over the PSF). The absolute accuracy of this latter estimation process is probably a few percent. We note that the relative photometry of different solar-type stars is set by the S/N of the individual measurements, which can be considerably more accurate than the absolute flux measurement.

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For targets with SEDs significantly different than solar-type, the LORRI calibration is dependent on the accuracy of the shape of LORRI's responsivity curve, as determined from the ground calibration (Morgan et al. 2005). As discussed there, we assumed that the wavelength dependence of the responsivity followed the prescriptions provided by the various vendors contributing to the LORRI hardware. While these prescriptions usually involved measurements made on actual LORRI hardware (e.g., transmittance measurements for the optical components), we assumed a QE curve for the CCD that followed the "typical" response specified by the manufacturer for the anti-reflection layer ordered for the LORRI CCD. The shape of the CCD QE curve is thought to be accurate to a few percent in the regions of high QE (i.e., for most of the wavelength range covered by LORRI), but larger variations in QE are possible in the steeply sloped portions of the QE curve. Given the wide bandpass of LORRI, these latter variations will likely not significantly affect the measured signals from LORRI's targets. For all these reasons, we suggest that the absolute accuracy for LORRI observations of non-solar-type targets is probably ~10%, and possibly significantly better than that, approaching the accuracy achieved for targets with solar-type SEDs.

For a photon counting optical system like LORRI, the signal detected (S_e in electrons) in an image pixel with exposure time t_exp (in seconds) can be expressed as:

$$\begin{eqnarray}&&{S}_{e}={t}_{\exp }\ast A\ast {\rm{\Omega }}\ast {\int }_{\lambda }I\ast \mathrm{QE}\ d\lambda \ \ (\mathrm{diffuse}\ \mathrm{target})\end{eqnarray} \tag{ 13 }$$

and:

$$\begin{eqnarray}&&{S}_{e}={t}_{\exp }\ast A\ast \mathrm{EE}\ast {\int }_{\lambda }F\ast \mathrm{QE}\ d\lambda \ (\mathrm{point}\ \mathrm{target})\end{eqnarray} \tag{ 14 }$$

where:

• A is the unobscured aperture area of the OTA (339.8 cm²).
• ${\rm{\Omega }}$ is the IFOV (2.464 × 10⁻¹¹ sr for 1 × 1, 3.942 × 10⁻¹⁰ sr for 4 × 4).
• I is the diffuse target radiance (photons cm⁻² s⁻¹ Å⁻¹ sr⁻¹).
• F is the point target flux (photons cm⁻² s.⁻¹ Å⁻¹).
• EE is the fraction of the point source flux captured in the peak pixel.
• QE is the total system quantum efficiency.

The noise (N in electrons) in a LORRI image pixel can be expressed as (for both diffuse and point targets):

$$\begin{eqnarray}&&N=\sqrt{{S}_{e}+{\rm{SL}}+{\rm{FT}}+({I}_{{\rm{d}}}\ast {t}_{\exp })+{{\rm{RN}}}^{2}}\end{eqnarray} \tag{ 15 }$$

where:

• SL is the signal produced by solar scattered light (e).
• FT is the signal produced by the CCD frame scrub and transfer process (i.e., smear) (e).
• I_d is the CCD dark current (e s⁻¹ pixel⁻¹).
• RN is the electronics noise (e, including the CCD read noise).

The LORRI solar scattered light level (SL) has been measured multiple times during the mission (Table 4). For solar elongation angles (SEAs) smaller than ~30°, the scattered light level varies as a function of the spacecraft roll angle. Figure 21 shows a model for the I/F of the solar scattered light level as a function of SEA. The model falls roughly halfway between the smallest and largest observed scattered light values. At small SEAs, the actual I/F of the solar scattered light could be up to a factor of two times smaller or larger than the model value. The model I/F values are independent of the spacecraft's heliocentric distance (r), but the CCD signal rate (DN s⁻¹) has an r⁻² dependence. The SEA at which the solar scattered light produces a signal rate of 10 DN s⁻¹ pixel⁻¹ (i.e., ~10× larger than the electronics noise) is shown in the figure for the heliocentric distances of the New Horizons flybys (i.e., at Jupiter, Pluto, and MU69).

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The LORRI team created an exposure time calculator (ETC) that uses the above formalism to estimate S/Ns for planned observations. The ETC can also be used estimate target signals in absolute units by comparing observed S/Ns to S/Ns reported by the ETC. For point sources with S/N ≥ 5 in a single pixel, the S/N can typically be improved by a factor of ~2 by summing the signal over several pixels (aperture photometry) or by employing PSF-fitting photometry.

The LORRI signal level depends on two key parameters: the total system quantum efficiency (QE) and (in the point source case) the amount of energy from a point source concentrated in a single pixel (EE). LORRI's EE was discussed in the previous subsection, so we focus on QE here.

For LORRI, the QE is given by:

$$\begin{eqnarray}&&\mathrm{QE}={L}_{\mathrm{obscure}}\ast {T}_{\mathrm{optics}}\ast {\mathrm{QE}}_{\mathrm{CCD}}\end{eqnarray} \tag{ 16 }$$

where:

• L_obscure is the loss factor associated with obscuration by the secondary mirror and OTA spider.
• T_optics is the total transmittance of all optical elements.
• QE_CCD is the quantum efficiency of the CCD.

Although not explicitly stated, all quantities in the equation above are a function of wavelength. Prior to any system calibration measurements, LORRI's QE was estimated from Equation (16) using component level measurements from manufacturers. The original LORRI ETC also relied on these component level measurements. The system level QE was determined from ground calibration measurements (Morgan et al. 2005), and those measurements were used to update the ETC. Subsequently, in-flight measurements of absolute calibration standard reference stars (see the previous section) were used to further refine LORRI's absolute responsivity. The final LORRI absolute calibration is essentially a hybrid product, with the wavelength dependence determined from the ground calibration (when filters could be used to restrict the wavelengths sampled) and with the absolute sensitivity determined by scaling the wavelength-dependent curve by whatever factor is needed to force a match between the predicted and observed LORRI signals for observations of the absolute calibration standard stars.

Figure 22 shows the LORRI system QE as a function of wavelength, as determined from the absolute calibration measurements of the solar-type reference star HD 37962. The LORRI system QE is approximately 50% over much of the visible wavelength range (e.g., 480–700 nm). LORRI is a panchromatic instrument, which means that its output signal is proportional to the integral over all wavelengths of the product of the QE and the target's SED.

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Note that the commonly used quantity "effective area" (A_eff) of the optical system is just the area of LORRI's input aperture ($A=\,\pi \ast {20.8}^{2}/4=339.8$ cm²) multiplied by the system QE. Given the estimated LORRI obscuration of ~11% (i.e., ${L}_{\mathrm{obscure}}=0.89$), the largest possible effective area for LORRI is ~300 cm². Figure 23 shows the LORRI effective area as a function of wavelength.

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The LORRI absolute responsivity curve, which is used to calculate the photometry keywords, can be derived from the QE curve using the following equation:

$$\begin{eqnarray}&&{R}_{\lambda }={A}_{\mathrm{eff}}\ast {\rm{\Omega }}\ast \lambda /\mathrm{gain}/{hc}\end{eqnarray} \tag{ 17 }$$

where:

• ${R}_{\lambda }$ is the responsivity ((DN s⁻¹ pixel⁻¹)/(erg cm⁻² s⁻¹ sr⁻¹)).
• A_eff is the effective area as defined above (cm²).
• ${\rm{\Omega }}$ is the solid angle of a single pixel (sr).
• $\lambda$ is the wavelength of interest (nm).
• gain is the CCD gain (21 e DN⁻¹ for 1 × 1 format).
• hc is the product of Planck's constant and the speed of light (1.986 × 10⁻¹⁶ J nm).

Figure 24 shows the LORRI responsivity curve as a function of wavelength for 1 × 1 format, as derived from the measurements of the absolute calibration standard star HD37962. The responsivity curve for 4 × 4 format can be obtained by multiplying the 1 × 1 curve by the constant 17.1.

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