Documentation – Current v26.1

Local Magnification Results


Results Documentation

This page provides documentation of results for Local Magnification in Imatest. 

For the associated target analysis (e.g., Checkerboard), the following data are included in the JSON and CSV result files under these fields:

  • JSON: local_magnification_data
  • CSV: [Local Magnification Data]

Note: The CSV files are encoded in UTF-8 and may contain characters like ° (degrees) and θ (theta). Some programs (notably Excel when opening CSVs directly) may assume a different encoding, causing characters to display incorrectly (e.g., ° → °). Open or import the file using UTF-8 to view it correctly.

Local Magnification Data

Description

The settings/data/results related to calculation of local magnification and associated metrics.

Result Field(s)

Title Description Validation Included In: Key JSON Type Note(s)
Calculation Settings The settings used to calculate local magnification and associated metrics.
  • JSON: calculation_settings
  • CSV: [Calculation Settings]
 object  
Image Size (Rows Columns) The image size (rows, columns).  
  • JSON: image_size_rows_columns
  • CSV: Image Size (Rows Columns)
 array of number  
Origin (XY) The image coordinate (X, Y) for the origin using the IEEE Std 2020 Type IV coordinate system.  
  • JSON: origin_xy_px
  • CSV: Origin (XY) [px]
 array of number
  • Units: px
Numeric Image Center (XY) The image coordinate (X, Y) for the numeric image center using the IEEE Std 2020 Type IV coordinate system.  
  • JSON: numeric_image_center_xy_px
  • CSV: Numeric Image Center (XY) [px]
 array of number
  • Units: px
Image Max Radius The maximum image radius in pixels.  
  • JSON: image_max_radius_px
  • CSV: Image Max Radius [px]
 number
  • Units: px
Image Max Radius The maximum image radius in millimeters.  
  • JSON: image_max_radius_mm
  • CSV: Image Max Radius [mm]
 number
  • Units: mm
Object Max Radius The estimated object radius (in grid steps) at the maximum image radius.  
  • JSON: object_max_radius_steps
  • CSV: Object Max Radius [steps]
 number
  • Units: steps
Object Max Radius The estimated object radius (in millimeters) at the maximum image radius.  
  • JSON: object_max_radius_mm
  • CSV: Object Max Radius [mm]
 number
  • Units: mm
Per-Radial Data The data corresponding to each radial direction.
  • JSON: per_radial_data
  • CSV: [Per-Radial Data.###]
 array of object
  • For CSV, HDF5, and/or XML outputs, the one-based index is appended to each entry as indicated by the ###.
Kx: Object Radius Normalization Scale Factor The scale factor used to convert object radius in millimeters to the normalized domain.  
  • JSON: kx_object_radius_normalization_scale_factor
  • CSV: Kx: Object Radius Normalization Scale Factor
 number  
Ky: Image Radius Normalization Scale Factor The scale factor used to convert image radius in millimeters to the normalized domain.  
  • JSON: ky_image_radius_normalization_scale_factor
  • CSV: Ky: Image Radius Normalization Scale Factor
 number  
Polynomial Fit: Boundary Object Radius The data for the initial polynomial fit (object radius in grid steps as a function of image radius in pixels) that’s used to estimate object radius at the maximum image radius.
  • JSON: polynomial_fit_boundary_object_radius
  • CSV: [Polynomial Fit: Boundary Object Radius]
 object  
Polynomial Fit: Forward The data for the forward polynomial fit (normalized image radius as a function of normalized object radius).
  • JSON: polynomial_fit_forward
  • CSV: [Polynomial Fit: Forward]
 object  
Polynomial Fit: Inverse The data for the inverse polynomial fit (normalized object radius as a function of normalized image radius).
  • JSON: polynomial_fit_inverse
  • CSV: [Polynomial Fit: Inverse]
 object  
Image Radius Outermost Sample The image radius (in pixels) corresponding to the outer limit of the observed data.  
  • JSON: image_radius_outermost_sample_px
  • CSV: Image Radius Outermost Sample [px]
 number
  • Units: px
Image Radius Outermost Sample The image radius (in millimeters) corresponding to the outer limit of the observed data.  
  • JSON: image_radius_outermost_sample_mm
  • CSV: Image Radius Outermost Sample [mm]
 number
  • Units: mm
Image Radius Outermost Sample The normalized image radius corresponding to the outer limit of the observed data.  
  • JSON: image_radius_outermost_sample
  • CSV: Image Radius Outermost Sample
 number  
Object Radius Outermost Sample The object radius (in grid steps) corresponding to the outer limit of the observed data.  
  • JSON: object_radius_outermost_sample_steps
  • CSV: Object Radius Outermost Sample [steps]
 number
  • Units: steps
Object Radius Outermost Sample The object radius (in millimeters) corresponding to the outer limit of the observed data.  
  • JSON: object_radius_outermost_sample_mm
  • CSV: Object Radius Outermost Sample [mm]
 number
  • Units: mm
Object Radius Outermost Sample The normalized object radius corresponding to the outer limit of the observed data.  
  • JSON: object_radius_outermost_sample
  • CSV: Object Radius Outermost Sample
 number  
Image Radius Aggregate Samples The aggregate image radius samples in pixels (averaged from each radial direction). This corresponds to data from Table 1 in the reference paper.  
  • JSON: image_radius_aggregate_samples_px
  • CSV: Image Radius Aggregate Samples [px]
 array of number
  • Units: px
Image Radius Aggregate Samples The aggregate image radius samples in millimeters (averaged from each radial direction).  
  • JSON: image_radius_aggregate_samples_mm
  • CSV: Image Radius Aggregate Samples [mm]
 array of number
  • Units: mm
Image Radius Aggregate Samples The aggregate normalized image radius samples (averaged from each radial direction) used for the forward and inverse polynomial fits. This corresponds to data from Table 1 in the reference paper.  
  • JSON: image_radius_aggregate_samples
  • CSV: Image Radius Aggregate Samples
 array of number  
Object Radius Aggregate Samples The aggregate object radius samples in grid steps (averaged from each radial direction). This corresponds to data from Table 1 in the reference paper.  
  • JSON: object_radius_aggregate_samples_steps
  • CSV: Object Radius Aggregate Samples [steps]
 array of number
  • Units: steps
Object Radius Aggregate Samples The aggregate object radius samples in millimeters (averaged from each radial direction).  
  • JSON: object_radius_aggregate_samples_mm
  • CSV: Object Radius Aggregate Samples [mm]
 array of number
  • Units: mm
Object Radius Aggregate Samples The aggregate normalized object radius samples (averaged from each radial direction) used for the forward and inverse polynomial fits. This corresponds to data from Table 1 in the reference paper.  
  • JSON: object_radius_aggregate_samples
  • CSV: Object Radius Aggregate Samples
 array of number  
MLR The local radial magnification at the aggregate radii. This corresponds to data from Table 1 in the reference paper.  
  • JSON: mlr
  • CSV: MLR
 array of number  
MLR (Center-normalized) The local radial magnification (center-normalized) at the aggregate radii. This corresponds to data from Table 1 in the reference paper.  
  • JSON: mlr_center_normalized
  • CSV: MLR (Center-normalized)
 array of number  
MLT The local tangential magnification at the aggregate radii. This corresponds to data from Table 1 in the reference paper.  
  • JSON: mlt
  • CSV: MLT
 array of number  
MLT (Center-normalized) The local tangential magnification (center-normalized) at the aggregate radii. This corresponds to data from Table 1 in the reference paper.  
  • JSON: mlt_center_normalized
  • CSV: MLT (Center-normalized)
 array of number  
DRAD The radial distortion percentage at the aggregate radii. This corresponds to data from Table 1 in the reference paper.  
  • JSON: drad_pct
  • CSV: DRAD [%]
 array of number
  • Units: %
Image Radius Profile The plot profile for image radius in pixels.  
  • JSON: image_radius_profile_px
  • CSV: Image Radius Profile [px]
 array of number
  • Units: px
Image Radius Profile The plot profile for image radius in millimeters.  
  • JSON: image_radius_profile_mm
  • CSV: Image Radius Profile [mm]
 array of number
  • Units: mm
Image Radius Profile The plot profile for normalized image radius.  
  • JSON: image_radius_profile
  • CSV: Image Radius Profile
 array of number  
Object Radius Profile The plot profile for object radius in grid steps.  
  • JSON: object_radius_profile_steps
  • CSV: Object Radius Profile [steps]
 array of number
  • Units: steps
Object Radius Profile The plot profile for object radius in millimeters.  
  • JSON: object_radius_profile_mm
  • CSV: Object Radius Profile [mm]
 array of number
  • Units: mm
Object Radius Profile The plot profile for normalized object radius.  
  • JSON: object_radius_profile
  • CSV: Object Radius Profile
 array of number  
MLR Profile The plot profile for local radial magnification.  
  • JSON: mlr_profile
  • CSV: MLR Profile
 array of number  
MLR Profile (Center-normalized) The plot profile for local radial magnification (center-normalized).  
  • JSON: mlr_profile_center_normalized
  • CSV: MLR Profile (Center-normalized)
 array of number  
MLT Profile The plot profile for local tangential magnification.  
  • JSON: mlt_profile
  • CSV: MLT Profile
 array of number  
MLT Profile (Center-normalized) The plot profile for local tangential magnification (center-normalized).  
  • JSON: mlt_profile_center_normalized
  • CSV: MLT Profile (Center-normalized)
 array of number  
DRAD profile The plot profile for radial distortion percentage.  
  • JSON: drad_profile_pct
  • CSV: DRAD profile [%]
 array of number
  • Units: %
TV Distortion Data The TV distortion data derived from local magnification data, included only if Compute TV Distortion is enabled..
  • JSON: tv_distortion_data
  • CSV: [TV Distortion Data]
 object  
Projection Classification Data The projection method classification and field of view (FOV) data derived from local magnification data, included only if Compute Projection Classification is enabled.
  • JSON: projection_classification_data
  • CSV: [Projection Classification Data]
 object  

Local Magnification Per-Radial Data

Description

The per-radial direction data used for local magnification.

Result Field(s)

Title Description Validation Included In: Key JSON Type Note(s)
Radial Direction The sampling direction for this radial.
  • Enumeration Members:
    • E
    • SE
    • S
    • SW
    • W
    • NW
    • N
    • NE
  • JSON: radial_direction
  • CSV: Radial Direction
 string  
X Coordinates The per-sample X coordinate along this radial direction using the IEEE Std 2020 Type IV coordinate system.  
  • JSON: x_coordinates_px
  • CSV: X Coordinates [px]
 array of number
  • Units: px
Y Coordinates The per-sample Y coordinate along this radial direction using the IEEE Std 2020 Type IV coordinate system.  
  • JSON: y_coordinates_px
  • CSV: Y Coordinates [px]
 array of number
  • Units: px
Image Radius The image-plane radii in pixels.  
  • JSON: image_radius_px
  • CSV: Image Radius [px]
 array of number
  • Units: px
Image Radius The image-plane radii in millimeters.  
  • JSON: image_radius_mm
  • CSV: Image Radius [mm]
 array of number
  • Units: mm
Image Radius The image-plane radii normalized by the max radius.  
  • JSON: image_radius
  • CSV: Image Radius
 array of number  
Object Radius The object-plane radii in lattice grid steps.  
  • JSON: object_radius_steps
  • CSV: Object Radius [steps]
 array of number
  • Units: steps
Object Radius The object-plane radii in millimeters.  
  • JSON: object_radius_mm
  • CSV: Object Radius [mm]
 array of number
  • Units: mm
Object Radius The object-plane radii normalized by the max radius.  
  • JSON: object_radius
  • CSV: Object Radius
 array of number  

Used In

Local Magnification Polynomial Data

Description

The polynomial fit data used for local magnification.

Result Field(s)

Title Description Validation Included In: Key JSON Type Note(s)
Degree The polynomial fit degree.  
  • JSON: degree
  • CSV: Degree
 number  
Coefficients The polynomial fit coefficients in decreasing power order.  
  • JSON: coefficients
  • CSV: Coefficients
 array of number  
R-squared The coefficient of determination (R²) for the polynomial fit.  
  • JSON: r_squared
  • CSV: R-squared
 number  
Adjusted R-squared The adjusted coefficient of determination (adjusted R²) for the polynomial fit.  
  • JSON: adjusted_r_squared
  • CSV: Adjusted R-squared
 number  

Used In

Local Magnification Projection Classification Data

Description

The projection method classification and field of view (FOV) data derived from local magnification data, included only if Compute Projection Classification is enabled.

Result Field(s)

Title Description Validation Included In: Key JSON Type Note(s)
Best Projection Model The canonical projection mapping that minimizes the RMS error against the measured radial data.
  • Enumeration Members:
    • R=tan(θ)
    • R=2⋅tan(θ/2)
    • R=θ
    • R=2⋅sin(θ/2)
    • R=sin(θ)
  • JSON: best_projection_model
  • CSV: Best Projection Model
 string  
Best Model RMSE The Root Mean Square Error (RMSE) between the normalized measured radii and the theoretical curve of the best-fitting projection model.  
  • JSON: best_model_rmse
  • CSV: Best Model RMSE
 number  
Field of View The estimated full field of view at the defined maximum image radius based on the input target distance.  
  • JSON: field_of_view_deg
  • CSV: Field of View [°]
 number
  • Units: °
Field Angles The discrete half field angles calculated at the aggregate radii based on the input target distance.  
  • JSON: field_angles_deg
  • CSV: Field Angles [°]
 array of number
  • Units: °

Used In

Local Magnification Settings

Description

Settings used to calculate local magnification and associated metrics.

Result Field(s)

Title Description Validation Included In: Key JSON Type Note(s)
Pixel Pitch The input Pixel Pitch setting. The image sensor pixel pitch in microns.  
  • JSON: pixel_pitch_um
  • CSV: Pixel Pitch [um]
 number
  • Units: um
Grid Pitch The input Grid Pitch setting. The physical spacing between adjacent grid lines on the target (e.g., the height of a checker) in millimeters.  
  • JSON: grid_pitch_mm
  • CSV: Grid Pitch [mm]
 number
  • Units: mm
Compute Projection Classification The input Compute Projection Classification setting. Enable to compute the field of view and classify the projection method.  
  • JSON: compute_projection_classification
  • CSV: Compute Projection Classification
 boolean  
Target Distance The input Target Distance setting. The physical distance between the camera entrance pupil and the target in millimeters.  
  • JSON: target_distance_mm
  • CSV: Target Distance [mm]
 number
  • Units: mm
Compute TV Distortion The input Compute TV Distortion setting. Enable to compute TV distortion metrics, including picture height distortion (DPH) and SMIA TV distortion (DSTV).  
  • JSON: compute_tv_distortion
  • CSV: Compute TV Distortion
 boolean  
Radial Directions The input Radial Directions setting. Radial (eight-way compass) directions used to collect samples for the polynomial fits. Starting from the point nearest to the numeric image center, samples are gathered along the selected directions out to the farthest detected point(s). Samples from the chosen directions are averaged by common grid-step distance before computing the polynomial fits.
  • Enumeration Members:
    • E
    • SE
    • S
    • SW
    • W
    • NW
    • N
    • NE
  • JSON: radial_directions
  • CSV: Radial Directions
 array of string  
Origin The input Origin setting. The origin used for distortion measurements.
  • Enumeration Members:
    • Centermost detected point
    • Numeric image center
  • JSON: origin
  • CSV: Origin
 string  
Max Radius The input Max Radius setting. The image boundary that defines the maximum image radius used for distortion measurements and normalization.
  • Enumeration Members:
    • Outermost detected point
    • Image sides (left/right)
    • Image sides (top/bottom)
    • Image corners
    • Specify radius (px) from origin
  • JSON: max_radius
  • CSV: Max Radius
 string  
Polynomial Fit Degree The input Polynomial Fit Degree setting. The degree/order of the polynomial fits used to describe the mappings between image radius and object radius. If Auto-Select Degree is enabled, this value is used as the cap for the associated degree search.  
  • JSON: polynomial_fit_degree
  • CSV: Polynomial Fit Degree
 number  
Auto-Select Degree: Boundary Fit The input Auto-Select Degree: Boundary Fit setting. Enable to automatically select the polynomial fit degree/order for the initial mapping (object radius in grid steps as a function of image radius in pixels) that’s used to estimate object radius at the chosen max image radius. Scans degrees 2-N (where N is capped by the chosen Polynomial Fit Degree or the available samples) and stops at the first fit that meets the chosen Minimum R². If none do, it uses the degree with the highest R². When disabled, the input Polynomial Fit Degree is used. A zero-intercept is not enforced for this fit.  
  • JSON: auto_select_degree_boundary_fit
  • CSV: Auto-Select Degree: Boundary Fit
 boolean  
Auto-Select Degree: Normalized Fits The input Auto-Select Degree: Normalized Fits setting. Enable to automatically select the polynomial fit degree/order for the mapping (normalized image radius as a function of normalized object radius) that’s used to compute local magnification, as well as its inverse. Scans degrees 2-N (where N is capped by the chosen Polynomial Fit Degree or the available samples) and stops at the first fit that meets the chosen Minimum R². If none do, it uses the degree with the highest R². When disabled, the input Polynomial Fit Degree is used. A zero-intercept is enforced for these fits.  
  • JSON: auto_select_degree_normalized_fits
  • CSV: Auto-Select Degree: Normalized Fits
 boolean  
Minimum R-squared The input Minimum R² setting. Specifies the minimum coefficient of determination (R²) the fit must achieve for Auto-Select Degree searches. When the chosen R² metric reaches or exceeds this value, the search stops early. If Use Adjusted R² is enabled, the threshold applies to adjusted R² instead of standard R². For zero-intercept fits, uncentered definitions of R²/adjusted R² are used.  
  • JSON: minimum_r_squared
  • CSV: Minimum R-squared
 number  
Use Adjusted R-squared The input Use Adjusted R² setting. Enable to have Auto-Select Degree evaluate using adjusted R² instead of standard R². When enabled, the Minimum R² is treated as Minimum Adjusted R².  
  • JSON: use_adjusted_r_squared
  • CSV: Use Adjusted R-squared
 boolean  

Used In

Local Magnification TV Distortion Data

Description

The TV distortion data derived from local magnification data, included only if Compute TV Distortion is enabled.

Result Field(s)

Title Description Validation Included In: Key JSON Type Note(s)
SMIA TV Distortion (Image) The averaged SMIA TV distortion computed from the true image sides/corners.  
  • JSON: smia_tv_distortion_image_pct
  • CSV: SMIA TV Distortion (Image) [%]
 number
  • Units: %
Picture Height Distortion (Image) The averaged picture height distortion computed from the true image sides/corners.  
  • JSON: picture_height_distortion_image_pct
  • CSV: Picture Height Distortion (Image) [%]
 number
  • Units: %
SMIA TV Distortion (Grid) The averaged SMIA TV distortion computed from the detected grid sides/corners.  
  • JSON: smia_tv_distortion_grid_pct
  • CSV: SMIA TV Distortion (Grid) [%]
 number
  • Units: %
Picture Height Distortion (Grid) The averaged picture height distortion computed from the detected grid sides/corners.  
  • JSON: picture_height_distortion_grid_pct
  • CSV: Picture Height Distortion (Grid) [%]
 number
  • Units: %
Per-corner Order The corner order used for subsequent per-corner results.  
  • JSON: per_corner_order
  • CSV: Per-corner Order
 array of string  
Per-corner SMIA TV Distortion (Image) The per-corner SMIA TV distortion computed from the true image sides/corners.  
  • JSON: per_corner_smia_tv_distortion_image_pct
  • CSV: Per-corner SMIA TV Distortion (Image) [%]
 array of number
  • Units: %
Per-corner Picture Height Distortion (Image) The per-corner picture height distortion computed from the true image sides/corners.  
  • JSON: per_corner_picture_height_distortion_image_pct
  • CSV: Per-corner Picture Height Distortion (Image) [%]
 array of number
  • Units: %
Per-corner SMIA TV Distortion (Grid) The per-corner SMIA TV distortion computed from the detected grid sides/corners.  
  • JSON: per_corner_smia_tv_distortion_grid_pct
  • CSV: Per-corner SMIA TV Distortion (Grid) [%]
 array of number
  • Units: %
Per-corner Picture Height Distortion (Grid) The per-corner picture height distortion computed from the detected grid sides/corners.  
  • JSON: per_corner_picture_height_distortion_grid_pct
  • CSV: Per-corner Picture Height Distortion (Grid) [%]
 array of number
  • Units: %

Used In