PART ONE: Design, launch, and operate optical Earth Observation Missions - A figure-of-merit cheat sheet for optical EO payloads.

This is the first blog of a series of posts that addresses the design and operational constraints of an optical Earth Observation payload.

Designing, launching, and operating an optical payload as part of an Earth Observation mission can be extremely rewarding. Just ask those that were part of the “first light” experience during the early days of an EO mission. The adrenaline rush you get when opening that first image is contagious. However, getting to that point takes considerable work, and many underestimate the system engineering effort required on a spacecraft level for an optical payload to perform optimally. From a mission success perspective, quite a few system parameters need optimization. This is even more true within the newspace era, where smaller satellites are the norm, and the expectations regarding spatial, radiometric, and spectral performance are enormous.

These expectations are sometimes expressed in a language devoid of sensor specifics:

“Measure the reflected sunlight from crops to detect a reflectance difference of less than 0.2% at a ground resolution of about 2m by 2m daily for all agricultural land, across the globe, between 9 am and 11 am (cloud cover permitting). These measurements shall be suitable for use in all frequently used vegetation and leaf indexes, and variations between the measurements of different instruments shall be less than 2.5%.”

Or it can be loaded with specifics:

“An instrument with a 5 m GSD from 500 km, a swath of 50 km, six or more spectral bands in the VNIR range, and an SNR of >100 in each band that will fit on a 6U CubeSat.”

However, in each case, the system engineer needs to translate these requirements into system and instrument-level parameters and, together with a program manager, verify that the solution will be within budget and delivered on time.

Cost-Performance: the figure-of-merit driver

A previous blog post stated that commercial-driven funding models drive most decisions when planning an EO mission within the newspace sector. In this case, most decisions are made around the desired cost point, leaving the performance in the cold. However, from a system’s engineering approach, meeting the mission objectives is the primary goal, and the payload’s performance (accuracy) must support these requirements.

However, finding the working space where the instrument’s accuracy meets the optimal cost-effectiveness point is challenging. It requires a deep understanding of the various instrument parameters and how they will influence the overall mission success.

One of the first steps when determining the optimal instrument accuracy vs cost-effectiveness point is to define the various figures-of-merit that will meet the mission objectives. As shown in this blog post, these figures-of-merit can’t be addressed in isolation. Ranking the requirements according to importance for achieving the overall mission objective will aid the payload design process considerably.

The Resolution Balancing Act

Optimizing for spatial, radiometric, spectral, and temporal resolution is a balancing act. What is more challenging is that each of these resolution components has a figure of merit that requires attention from a system’s engineering perspective.

Spatial Resolution: Although most people will quote GSD on a system level, the actual figure of merit for spatial resolution is the Modulation Transfer Function (MTF). Ground Resolved Distance (GRD) is also frequently used and is an excellent way to determine if the quoted GSD is a realistic value to achieve.
Radiometric Resolution: The expected Signal-to-Noise Ratio is frequently used but is only valid for a specific condition. Whereas Noise-Equivalent figure-of-merits help define the particular sensitivity requirements of an instrument. For example, Noise-Equivalent-Reflectance-Difference provides a good indication of the minimum variation in reflectance that could be detected.
Spectral Resolution: How well you need to capture the object under surveillance’s spectral signature determines the number of spectral bands, the width of each band, and the spectral range. In some domains, the spectral content and possible variation in the spectrum of the objects under surveillance are well known. In these cases, like vegetation monitoring, the spectral resolution is well-defined, and industry norms can be used. When this is not the case, more bands with narrower bandwidths across the spectral range are required.
Temporal Resolution: When using Earth Observation for change monitoring, understanding the rate at which change happen is a critical input in designing an EO mission. For instance, in the agricultural sector, change can happen overnight. Another part of the equation is capturing global data from the same area while reducing latency. The “everywhere” vs. “anywhere” revisiting principle is another essential operational concept that needs to be addressed.

Addressing System Parameters to Optimize Figure-of-Merits.

Various parameters define the resolution performance criteria of an EO optical system. The effective aperture diameter may be the most important as it determines the diffraction limit and energy entering the system. However, this parameter can’t be optimized in isolation and should be evaluated with the other parameters in the following table. This table provides a short overview of the most critical parameters that need to be defined during the design stages of an optical system and impacts the mission’s accuracy and performance criteria. However, these parameters must be addressed with the physical and environmental constraints and, most importantly, the budget.

	SPATIAL ACCURACY	RADIOMETRIC ACCURACY	SPECTRAL ACCURACY	TEMPORAL ACCURACY
Effective Aperture Diameter	Larger aperture results in a higher diffraction limit which will directly impact MTF.	The larger the aperture area or, the smaller the F#, the more photons the signal can be captured.	The effective aperture of the system determines the optical transmission, which is a function of wavelength.	The effective aperture, including the effect of an obscuration, directly impacts the size of the field area and, therefore, the swath.
Focal Length	GSD scales indirectly with focal length; F# scales directly with focal length. [GSD = Orbital Height x Pixel Pitch / Focal Length]	Focal length directly impacts F#, indirectly impacting the number of photons captured per exposure time.	Limited to no impact on spectral accuracy.	The focal length impacts the swath for pixel pitch and detector size.
F-number	The focal length-to-diameter ratio impacts the MTF, GRD, and SNR.	A lower F# increases the radiometric accuracy for a given system.	Limited to no impact on spectral accuracy.	Little to no effect on temporal accuracy.
Pixel Pitch	The pixel size and GSD are directly proportional—the smaller the pixel smaller the GSD, but the higher the spatial Nyquist Frequency.	Smaller pixels result in a smaller full-well capacity and directly impact the dynamic range and the signal saturation levels.	The pixel size and photodiode technology directly impact the QE, which affects the overall spectral response.	The pixel pitch and the number of pixels determine the instrument’s GSD and swath width. They are increasing the swath results in higher temporal frequency.
Orbit Height	The orbital height has a direct impact on GSD and GRD.	Orbital altitude determines the nadir GSD and directly impacts the instantaneous exposure time.	Limited to no effect on spectral accuracy.	Orbital parameters have a direct impact on the satellite swath and revisit time.
Wavelength	Longer wavelengths result in lower diffraction limits [MTF, GRD]	The specific wavelength of a photon determines the energy of the photon (E=hc/λ) – The longer the wavelength, the less energy.	The wavelength determines the end-to-end optical system design, response, and performance, influencing spectral accuracy.	Limited to no impact on temporal precision.
Exposure Time	An increase in exposure time has a direct impact on spacecraft stability requirements.	The longer the exposure time, the more photons and electrons can be captured.	It will limit the number of spectral bands captured with a single detector in a specific exposure time.	Little to no impact on temporal accuracy.
Quantum Efficiency	QE has a minimal impact on spatial accuracy.	A higher QE results in more photons converted into electrons.	QE is wavelength depended and may have a direct effect on spectral accuracy. Therefore, the QE must be accounted for to determine the end-to-end spectral response.	Limited to no impact on temporal precision.
# TDI Steps	An increase in # of TDI stages directly impacts spacecraft stability requirements.	The increase in digital TDI stages decreases noise levels, increasing SNR.	Limited to no impact on spectral accuracy.	Little to no effect on temporal precision.
# Bands	Different bands have different diffraction limits. See the effect of longer wavelengths on the diffraction limit.	The number of bands may directly impact the FWHM and the total energy transmitted through the system.	The number of bands, together with the bandwidth, determines the amount of information to be extracted. More bands may be required if the spectral content has a high variation.	Little to no impact on temporal accuracy.
FWHM	Different bands and bandwidths directly impact the system’s diffraction limit and MTF and GRD.	The energy and photons transmitted through the system are proportional to the spectral bandwidth.	The spectral bandwidth determines the slightest variation in spectral content be detected.	Little to no impact on temporal accuracy.
Swath	It may increase the geospatial and geolocation accuracy. However, a wide swath may impact overall MTF performance.	The increase in swath may decrease the total transmittance of the system due to an increase in obscuration size.	Little to no impact on spectral accuracy.	The instrument swath directly impacts the number of satellites required to increase revisit frequency.
# Satellites	It may increase the geospatial and geolocation accuracy.	An increase in the number of satellites directly impacts the radiometric calibration accuracy between satellites.	Spectral calibration between satellites becomes trickier with increased spectral resolution and the number of satellites.	The higher the number of satellites, the lower the revisit time.

A flow-down optical payload design methodology

Optimizing each parameter to find the optimal spatial, radiometric, spectral, and temporal resolution working point is an iterative process, as indicated in Figure 1. Derived system requirements, physical and environmental constraints, and technology assumptions are essential when developing an optical system. This design flow is also critical to understand when developing a mission and the concept of operations of an optical EO mission.

For an optical system it is necessary to relate the system requirements to lower-level requirements that summarize the sensor performance and list the design parameters. During this process, assumptions are made regarding the focal plane assembly and configuration, optomechanical parameters and performance, sensor technology, and spectral radiance. The assumptions are input to a noise, MTF, and data model that are assessed and compared against the system requirements. After the assessment, the design process is iterated until the optimal cost-benefit vs. accuracy point is reached (See Ref. 1).

Although Simera Sense produce and market off-the-shelf optical payloads, we do provide our customers various tools to assist them with this design iteration process. One of these tools is a system level workbook that calculates all the parameters mentioned in cheat-sheet. Furthermore, this workbook guides our clients to make decisions regarding the required attitude determination and control system, expected spatial and noise performance, and data delivery capacity.

Feel free to contact us if you require more information regarding this workbook: info@simera-sense.com.

Terrence S. Lomheim et al., Translation of spectral radiance levels. band choices, and signal-to-noise requirements to focal plane specifications and design constraints, Proc. of SPIE, Vol. 4486, Infrared Spaceborne Remote Sensing IX, February 2002.