analysis.spot_diagram

Spot Diagram Analysis Package

This package provides spot diagram analysis for optical systems, including configurable reference centering strategies.

class SpotData(x: array, y: array, intensity: array)

Stores the x, y coordinates and intensity of a spot.

x

Array of x-coordinates.

Type:

optiland.backend.numpy_backend.NumpyBackend.array

y

Array of y-coordinates.

Type:

optiland.backend.numpy_backend.NumpyBackend.array

intensity

Array of intensity values.

Type:

optiland.backend.numpy_backend.NumpyBackend.array

intensity: array

x: array

y: array

class SpotDiagram(optic, fields: str | list = 'all', wavelengths: str | list = 'all', num_rings: int = 6, distribution: DistributionType = 'hexapolar', coordinates: Literal['global', 'local'] = 'local', reference: str | SpotReferenceType = SpotReferenceType.CHIEF_RAY)

Generates and plots real ray intersection data on the image surface.

This class creates spot diagrams, which are purely geometric plots that give an indication of the blur produced by aberrations in an optical system.

optic

Instance of the optic object to be assessed.

fields

Fields at which data is generated.

wavelengths

Wavelengths at which data is generated.

num_rings

Number of rings in the pupil distribution for ray tracing.

distribution

The pupil distribution type for ray tracing.

data

Contains spot data in a nested list, ordered by field, then wavelength.

coordinates

The coordinate system (‘global’ or ‘local’) for data and plotting.

reference

The reference point type used for centering spots.

airy_disc_x_y(wavelength: float) → tuple[list[float], list[float]]

Generates the Airy disk radii for the x and y axes for each field.

Parameters:

wavelength – The wavelength for the calculation.

Returns:

x-axis radii and y-axis radii per field.

Return type:

A tuple of two lists

airy_radius(n_w: float, wavelength: float) → float

Calculates the Airy disk radius.

Parameters:

• n_w – The physical F-number.

• wavelength – The wavelength of light in micrometers.

Returns:

The Airy disk radius.

angle_from_cosine(a: BEArray, b: BEArray) → float

Calculates the angle in radians between two direction cosine vectors.

Parameters:

• a – The first direction cosine vector.

• b – The second direction cosine vector.

Returns:

The angle between the vectors in radians.

centroid() → list[tuple[BEArray, BEArray]]

Calculates the geometric centroid of each spot for the reference wavelength.

Returns:

A list of (x, y) centroid coordinates for each field.

f_number(n: float, theta: float) → float

Calculates the physical F-number.

Parameters:

• n – The refractive index of the medium.

• theta – The half-angle of the cone of light in radians.

Returns:

The calculated physical F-number.

generate_chief_rays_centers(wavelength: float) → BEArray

Generates the (x, y) intersection points for the chief ray of each field.

Parameters:

wavelength – The wavelength for the rays.

Returns:

An array of shape (num_fields, 2) with (x, y) coordinates.

generate_chief_rays_cosines(wavelength: float) → BEArray

Generates direction cosines for the chief ray of each field.

Parameters:

wavelength – The wavelength for the rays.

Returns:

An array of shape (num_fields, 3) containing the direction cosines.

generate_marginal_rays(H_x: float, H_y: float, wavelength: float) → tuple

Generates marginal rays at the four cardinal points of the pupil.

Parameters:

• H_x – The x-field coordinate.

• H_y – The y-field coordinate.

• wavelength – The wavelength for the rays.

Returns:

A tuple containing the traced rays for north, south, east, and west pupil points.

generate_marginal_rays_cosines(H_x: float, H_y: float, wavelength: float) → tuple

Generates direction cosines for each marginal ray of a given field.

Parameters:

• H_x – The x-field coordinate.

• H_y – The y-field coordinate.

• wavelength – The wavelength for the rays.

Returns:

A tuple of direction cosine vectors for north, south, east, and west rays.

geometric_spot_radius() → list[list[BEArray]]

Calculates the maximum geometric spot radius for each spot.

Returns:

A nested list of maximum radii for each field and wavelength.

rms_spot_radius() → list[list[BEArray]]

Calculates the root-mean-square (RMS) spot radius for each spot.

Returns:

A nested list of RMS radii for each field and wavelength.

view(fig_to_plot_on: Figure | None = None, figsize: tuple[float, float] = (12, 4), add_airy_disk: bool = False, *, show: bool = True) → tuple[Figure, list[Axes]]

Displays the spot diagram plot.

Parameters:

• fig_to_plot_on – An existing Matplotlib figure to plot on. If None, a new figure is created. Defaults to None.

• figsize – The figure size for the output window, applied per row. Defaults to (12, 4).

• add_airy_disk – If True, adds the Airy disk visualization to the plots. Defaults to False.

• show (bool) – If True (default), calls plt.show(). Set False for headless use.

Returns:

A tuple containing the Matplotlib figure and a list of its axes.

class SpotReferenceType(value, names=<not given>, *values, module=None, qualname=None, type=None, start=1, boundary=None)

Defines the available reference point types for spot centering.

CENTROID = 'centroid'

CHIEF_RAY = 'chief_ray'

capitalize()

Return a capitalized version of the string.

More specifically, make the first character have upper case and the rest lower case.

casefold()

Return a version of the string suitable for caseless comparisons.

center(width, fillchar=' ', /)

Return a centered string of length width.

Padding is done using the specified fill character (default is a space).

count(sub[, start[, end]]) → int

Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.

encode(encoding='utf-8', errors='strict')

Encode the string using the codec registered for encoding.

encoding

The encoding in which to encode the string.

errors

The error handling scheme to use for encoding errors. The default is ‘strict’ meaning that encoding errors raise a UnicodeEncodeError. Other possible values are ‘ignore’, ‘replace’ and ‘xmlcharrefreplace’ as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.

endswith(suffix[, start[, end]]) → bool

Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.

expandtabs(tabsize=8)

Return a copy where all tab characters are expanded using spaces.

If tabsize is not given, a tab size of 8 characters is assumed.

find(sub[, start[, end]]) → int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

format(*args, **kwargs) → str

Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces (‘{’ and ‘}’).

format_map(mapping) → str

Return a formatted version of S, using substitutions from mapping. The substitutions are identified by braces (‘{’ and ‘}’).

index(sub[, start[, end]]) → int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Raises ValueError when the substring is not found.

isalnum()

Return True if the string is an alpha-numeric string, False otherwise.

A string is alpha-numeric if all characters in the string are alpha-numeric and there is at least one character in the string.

isalpha()

Return True if the string is an alphabetic string, False otherwise.

A string is alphabetic if all characters in the string are alphabetic and there is at least one character in the string.

isascii()

Return True if all characters in the string are ASCII, False otherwise.

ASCII characters have code points in the range U+0000-U+007F. Empty string is ASCII too.

isdecimal()

Return True if the string is a decimal string, False otherwise.

A string is a decimal string if all characters in the string are decimal and there is at least one character in the string.

isdigit()

Return True if the string is a digit string, False otherwise.

A string is a digit string if all characters in the string are digits and there is at least one character in the string.

isidentifier()

Return True if the string is a valid Python identifier, False otherwise.

Call keyword.iskeyword(s) to test whether string s is a reserved identifier, such as “def” or “class”.

islower()

Return True if the string is a lowercase string, False otherwise.

A string is lowercase if all cased characters in the string are lowercase and there is at least one cased character in the string.

isnumeric()

Return True if the string is a numeric string, False otherwise.

A string is numeric if all characters in the string are numeric and there is at least one character in the string.

isprintable()

Return True if all characters in the string are printable, False otherwise.

A character is printable if repr() may use it in its output.

isspace()

Return True if the string is a whitespace string, False otherwise.

A string is whitespace if all characters in the string are whitespace and there is at least one character in the string.

istitle()

Return True if the string is a title-cased string, False otherwise.

In a title-cased string, upper- and title-case characters may only follow uncased characters and lowercase characters only cased ones.

isupper()

Return True if the string is an uppercase string, False otherwise.

A string is uppercase if all cased characters in the string are uppercase and there is at least one cased character in the string.

join(iterable, /)

Concatenate any number of strings.

The string whose method is called is inserted in between each given string. The result is returned as a new string.

Example: ‘.’.join([‘ab’, ‘pq’, ‘rs’]) -> ‘ab.pq.rs’

ljust(width, fillchar=' ', /)

Return a left-justified string of length width.

Padding is done using the specified fill character (default is a space).

lower()

Return a copy of the string converted to lowercase.

lstrip(chars=None, /)

Return a copy of the string with leading whitespace removed.

If chars is given and not None, remove characters in chars instead.

static maketrans()

Return a translation table usable for str.translate().

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters to Unicode ordinals, strings or None. Character keys will be then converted to ordinals. If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

partition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing the original string and two empty strings.

removeprefix(prefix, /)

Return a str with the given prefix string removed if present.

If the string starts with the prefix string, return string[len(prefix):]. Otherwise, return a copy of the original string.

removesuffix(suffix, /)

Return a str with the given suffix string removed if present.

If the string ends with the suffix string and that suffix is not empty, return string[:-len(suffix)]. Otherwise, return a copy of the original string.

replace(old, new, count=-1, /)

Return a copy with all occurrences of substring old replaced by new.

count

Maximum number of occurrences to replace. -1 (the default value) means replace all occurrences.

If the optional argument count is given, only the first count occurrences are replaced.

rfind(sub[, start[, end]]) → int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

rindex(sub[, start[, end]]) → int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Raises ValueError when the substring is not found.

rjust(width, fillchar=' ', /)

Return a right-justified string of length width.

Padding is done using the specified fill character (default is a space).

rpartition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string, starting at the end. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing two empty strings and the original string.

rsplit(sep=None, maxsplit=-1)

Return a list of the substrings in the string, using sep as the separator string.

sep

The separator used to split the string.

When set to None (the default value), will split on any whitespace character (including n r t f and spaces) and will discard empty strings from the result.

maxsplit

Maximum number of splits. -1 (the default value) means no limit.

Splitting starts at the end of the string and works to the front.

rstrip(chars=None, /)

Return a copy of the string with trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

split(sep=None, maxsplit=-1)

Return a list of the substrings in the string, using sep as the separator string.

sep

The separator used to split the string.

When set to None (the default value), will split on any whitespace character (including n r t f and spaces) and will discard empty strings from the result.

maxsplit

Maximum number of splits. -1 (the default value) means no limit.

Splitting starts at the front of the string and works to the end.

Note, str.split() is mainly useful for data that has been intentionally delimited. With natural text that includes punctuation, consider using the regular expression module.

splitlines(keepends=False)

Return a list of the lines in the string, breaking at line boundaries.

Line breaks are not included in the resulting list unless keepends is given and true.

startswith(prefix[, start[, end]]) → bool

Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.

strip(chars=None, /)

Return a copy of the string with leading and trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

swapcase()

Convert uppercase characters to lowercase and lowercase characters to uppercase.

title()

Return a version of the string where each word is titlecased.

More specifically, words start with uppercased characters and all remaining cased characters have lower case.

translate(table, /)

Replace each character in the string using the given translation table.

table

Translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, strings, or None.

The table must implement lookup/indexing via __getitem__, for instance a dictionary or list. If this operation raises LookupError, the character is left untouched. Characters mapped to None are deleted.

upper()

Return a copy of the string converted to uppercase.

zfill(width, /)

Pad a numeric string with zeros on the left, to fill a field of the given width.

The string is never truncated.