All satellite imaging sensors suffer from a fundamental limitation; the Digital Number (DN) recorded by a pixel does not only measure radiance originating from the area of the Earth’s surface represented by this pixel, but it also measures radiance originating from surrounding areas represented by adjacent pixels.

This adjacency effect impacts image processing algorithms that characterize the Earth’s surface on a per-pixel basis. These algorithms usually neglect the adjacency effect and assume an ideal pixel for which 100 % of its DN originates from the area represented by this pixel. This “ideal pixel” assumption is equivalent to stating that the spatial resolution of the image is equal to the ground pixel size or Ground Sampling Distance (GSD).

The ideal pixel assumption generates moderate errors for satellite imagers in which the spatial response of the sensor is limited by the spatial response of its detector, but it generates gross errors for satellite imagers in which the spatial response of the imaging sensor is limited by the spatial response of its optical aperture.

Traditional large remote sensing satellites (few tons in weight) deployed by space agencies, such as Landsat, provide images that usually have a detector-limited response, whereas the more recent small CubeSat satellites (few kilograms in weight) deployed by commercial vendors, such as Planet’s SuperDove, provide images that usually have an optics limited response.

As demonstrated in the sixth chapter, in a Landsat image about 70 % of a pixel’s DN originates from the area represented by this pixel, and its average spatial resolution distance is about 1.5 times larger than its GSD. In a SuperDove image about 10 % of a pixel’s DN originates from the area represented by this pixel, and the average spatial resolution distance is about five times larger than its GSD.

The early satellite images had a detector-limited response, so the moderate errors of the ideal pixel assumption were almost unnoticeable, being mostly masked by image noise. The models (metrics, methods, and algorithms) associated with this assumption were adopted as axioms, and although some works warned about the errors involved in using these models to describe optics-limited images, these warnings went unnoticed by most of the remote sensing community.

The aim of this research is to advance the assessment of the spatial response of satellite images by developing four innovations applicable to detector-limited and optics-limited images:
(1) a metric to gauge spatial resolution distance,
(2) a method to assess spatial response models,
(3) a model to estimate spatial response from edge measurements, and
(4) a procedure to improve the spatial response of satellite images.

The first chapter of this thesis presents the genesis of the problem, introduces some key technical terms that will be used in the next chapters, and gives an overall view of my research.

The second chapter presents an upgraded taxonomy of spatial resolution metrics and develops a new metric that computes the spatial resolution distance as a function the image’s resolving contrast. This new metric allows current spatial resolution metrics to be assessed using an unbiased framework, showing that most current metrics are either incorrect or biased.

The third chapter shows that the current methodology to assess spatial response models is biased since it uses as a benchmark a specific sensor with a given spatial response, so the model’s assessment is only applicable to this specific spatial response. This chapter develops a new methodology that uses the optical design parameters – which define the spatial response – as independent variables, so the assessment is applicable to a wide variety of spatial responses. This methodology is applied to assess the two-edge Separable Point Spread Function (PSF) model that estimates the spatial response of a satellite image by measuring this response along two perpendicular edges. It is shown that this popular two-edge model is only applicable to low optical factors (detector-limited images) and that it gives incorrect results for the higher optical factors (optic-limited images) employed by most types of current satellite images.

The fourth chapter develops a new spatial response model that uses three edge measurements and that is applicable to the higher optical factors not covered by the Separable PSF model. This new three-edge model is developed and assessed with the same methodology developed in the third chapter, showing that it complements the two-edge model, so that both models together enable the estimation of the spatial response through edge measurement for all optical factors.

The adjacency errors of the ideal pixel assumption can be reduced by “restoration”, an image processing technique that approximates the actual image to the ideal image. The usual restoration technique deconvolves the raw image with a deconvolution kernel defined by the sensor’s spatial response. It has been shown that this usual kernel is not optimal and an empirical method to find the optimum kernel has been proposed, but this method is cumbersome and is not applicable to all satellite imagers. In response to this limitation, the fifth chapter develops a new alternative method to find the optimum kernel by using synthetic edge images. This new method is validated by showing that its predictions agree with the results of the previous empirical method. The new method is more accurate and simpler to apply, opening new research paths on image restoration.
The sixth chapter demonstrates the practical application of the metric developed in the second chapter, by computing the spatial resolution distance of the green channels’ images captured by SuperDove and Landsat 8 satellites, under three different conditions: (1) negligible atmospheric turbulence and moderate spacecraft jitter, (2) strong atmospheric turbulence and moderate spacecraft jitter, (3) negligible atmospheric turbulence and high spacecraft jitter. An original procedure is developed to estimate the spatial response model of the imaging channels, by using a combination of spatial response measurements, known sensor parameters, and unknown sensor parameters.

The seventh chapter synthetizes the results, illustrating new applications for the innovations presented in the previous chapters and giving examples how they can be used altogether as tools to improve the assessment and the quality of satellite images.