plate scale
Definition: Plate scale denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Multiplying the plate scale by a detector’s physical pixel size (in mm) gives the pixel scale in arcsec/pixel -- the practical number that determines both a camera’s field of view (pixel scale × detector width) and its ability to resolve fine structure.
Why it matters here: Lecture 02 fixed how sharp an image a telescope can in principle deliver. This lecture answers the practical question every instrument designer must solve next: how large, in millimeters, does that sharp image actually appear at the focal plane, and how small must a detector’s pixels be to record it without throwing resolution...
Relationships: It is used with pixel scale to interpret the lecture model. The quantitative connection is the working relation \(s = \dfrac{206265^{\prime\prime}}{f\,[\mathrm{mm}]}, \qquad \text{pixel scale} = s \times p\,[\mathrm{mm}], \qquad \text{Nyquist: pixel scale} \le \dfrac{\mathrm{FWHM}}{2}\).
Boundary or common confusion: Assuming a smaller pixel is always better. Undersampling wastes optical resolution, but excessively small pixels (oversampling) spread the same total signal across more pixels, each carrying its own read-noise contribution (Lecture 05), which can lower the effective signal-to-noise ratio for faint sources without any corresponding gain in usable resolution...
pixel scale
Definition: Pixel scale denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Multiplying the plate scale by a detector’s physical pixel size (in mm) gives the pixel scale in arcsec/pixel -- the practical number that determines both a camera’s field of view (pixel scale × detector width) and its ability to resolve fine structure.
Why it matters here: Lecture 02 fixed how sharp an image a telescope can in principle deliver. This lecture answers the practical question every instrument designer must solve next: how large, in millimeters, does that sharp image actually appear at the focal plane, and how small must a detector’s pixels be to record it without throwing resolution...
Relationships: It is used with plate scale, field of view to interpret the lecture model. The quantitative connection is the working relation \(s = \dfrac{206265^{\prime\prime}}{f\,[\mathrm{mm}]}, \qquad \text{pixel scale} = s \times p\,[\mathrm{mm}], \qquad \text{Nyquist: pixel scale} \le \dfrac{\mathrm{FWHM}}{2}\).
Boundary or common confusion: Assuming a smaller pixel is always better. Undersampling wastes optical resolution, but excessively small pixels (oversampling) spread the same total signal across more pixels, each carrying its own read-noise contribution (Lecture 05), which can lower the effective signal-to-noise ratio for faint sources without any corresponding gain in usable resolution...
field of view
Definition: Field of view denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Multiplying the plate scale by a detector’s physical pixel size (in mm) gives the pixel scale in arcsec/pixel -- the practical number that determines both a camera’s field of view (pixel scale × detector width) and its ability to resolve fine structure.
Why it matters here: Lecture 02 fixed how sharp an image a telescope can in principle deliver. This lecture answers the practical question every instrument designer must solve next: how large, in millimeters, does that sharp image actually appear at the focal plane, and how small must a detector’s pixels be to record it without throwing resolution...
Relationships: It is used with pixel scale, focal plane to interpret the lecture model. The quantitative connection is the working relation \(s = \dfrac{206265^{\prime\prime}}{f\,[\mathrm{mm}]}, \qquad \text{pixel scale} = s \times p\,[\mathrm{mm}], \qquad \text{Nyquist: pixel scale} \le \dfrac{\mathrm{FWHM}}{2}\).
Boundary or common confusion: Assuming a smaller pixel is always better. Undersampling wastes optical resolution, but excessively small pixels (oversampling) spread the same total signal across more pixels, each carrying its own read-noise contribution (Lecture 05), which can lower the effective signal-to-noise ratio for faint sources without any corresponding gain in usable resolution...
focal plane
Definition: Focal plane denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: A small angle θ (radians) subtended on the sky is imaged, by simple similar-triangles geometry through a telescope of effective focal length f, onto a physical size x = fθ at the focal plane; converting θ to arcseconds and f to millimeters gives the standard plate-scale relation s =...
Why it matters here: Lecture 02 fixed how sharp an image a telescope can in principle deliver. This lecture answers the practical question every instrument designer must solve next: how large, in millimeters, does that sharp image actually appear at the focal plane, and how small must a detector’s pixels be to record it without throwing resolution...
Relationships: It is used with field of view, Nyquist sampling to interpret the lecture model. The quantitative connection is the working relation \(s = \dfrac{206265^{\prime\prime}}{f\,[\mathrm{mm}]}, \qquad \text{pixel scale} = s \times p\,[\mathrm{mm}], \qquad \text{Nyquist: pixel scale} \le \dfrac{\mathrm{FWHM}}{2}\).
Boundary or common confusion: Assuming a smaller pixel is always better. Undersampling wastes optical resolution, but excessively small pixels (oversampling) spread the same total signal across more pixels, each carrying its own read-noise contribution (Lecture 05), which can lower the effective signal-to-noise ratio for faint sources without any corresponding gain in usable resolution...
Nyquist sampling
Definition: Nyquist sampling denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: The Nyquist sampling criterion, borrowed directly from signal processing, requires at least two pixels across the FWHM of the smallest resolvable feature (the diffraction-limited or seeing-limited PSF) to avoid throwing away resolution the optics already deliver (undersampling), while...
Why it matters here: Lecture 02 fixed how sharp an image a telescope can in principle deliver. This lecture answers the practical question every instrument designer must solve next: how large, in millimeters, does that sharp image actually appear at the focal plane, and how small must a detector’s pixels be to record it without throwing resolution...
Relationships: It is used with focal plane, undersampling to interpret the lecture model. The quantitative connection is the working relation \(s = \dfrac{206265^{\prime\prime}}{f\,[\mathrm{mm}]}, \qquad \text{pixel scale} = s \times p\,[\mathrm{mm}], \qquad \text{Nyquist: pixel scale} \le \dfrac{\mathrm{FWHM}}{2}\).
Boundary or common confusion: Assuming a smaller pixel is always better. Undersampling wastes optical resolution, but excessively small pixels (oversampling) spread the same total signal across more pixels, each carrying its own read-noise contribution (Lecture 05), which can lower the effective signal-to-noise ratio for faint sources without any corresponding gain in usable resolution...
undersampling
Definition: Undersampling denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: The Nyquist sampling criterion, borrowed directly from signal processing, requires at least two pixels across the FWHM of the smallest resolvable feature (the diffraction-limited or seeing-limited PSF) to avoid throwing away resolution the optics already deliver (undersampling), while...
Why it matters here: Lecture 02 fixed how sharp an image a telescope can in principle deliver. This lecture answers the practical question every instrument designer must solve next: how large, in millimeters, does that sharp image actually appear at the focal plane, and how small must a detector’s pixels be to record it without throwing resolution...
Relationships: It is used with Nyquist sampling, oversampling to interpret the lecture model. The quantitative connection is the working relation \(s = \dfrac{206265^{\prime\prime}}{f\,[\mathrm{mm}]}, \qquad \text{pixel scale} = s \times p\,[\mathrm{mm}], \qquad \text{Nyquist: pixel scale} \le \dfrac{\mathrm{FWHM}}{2}\).
Boundary or common confusion: Assuming a smaller pixel is always better. Undersampling wastes optical resolution, but excessively small pixels (oversampling) spread the same total signal across more pixels, each carrying its own read-noise contribution (Lecture 05), which can lower the effective signal-to-noise ratio for faint sources without any corresponding gain in usable resolution...
oversampling
Definition: Oversampling denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: The Nyquist sampling criterion, borrowed directly from signal processing, requires at least two pixels across the FWHM of the smallest resolvable feature (the diffraction-limited or seeing-limited PSF) to avoid throwing away resolution the optics already deliver (undersampling), while...
Why it matters here: Lecture 02 fixed how sharp an image a telescope can in principle deliver. This lecture answers the practical question every instrument designer must solve next: how large, in millimeters, does that sharp image actually appear at the focal plane, and how small must a detector’s pixels be to record it without throwing resolution...
Relationships: It is used with undersampling to interpret the lecture model. The quantitative connection is the working relation \(s = \dfrac{206265^{\prime\prime}}{f\,[\mathrm{mm}]}, \qquad \text{pixel scale} = s \times p\,[\mathrm{mm}], \qquad \text{Nyquist: pixel scale} \le \dfrac{\mathrm{FWHM}}{2}\).
Boundary or common confusion: Assuming a smaller pixel is always better. Undersampling wastes optical resolution, but excessively small pixels (oversampling) spread the same total signal across more pixels, each carrying its own read-noise contribution (Lecture 05), which can lower the effective signal-to-noise ratio for faint sources without any corresponding gain in usable resolution...