Setting a Measure

What is a Measure?

A Measure is the formula of measure calculation to determine the numerical value of the physical quantity, the notion or the function selected.

How to set a Measure?

Setting one measure to an area

Select the area to measure.
From the Measure list, select the measure to set.

Setting several measures to an area

Select the Measure cell of the area for which to add another measure.
Click Add area or measure .
From the Measure list, select the measure to set.

What are the measures available?

The topic considers photometric units and maps. If you make radiometric analysis, the units and maps correspondence are:


Unit		Map
Photometric	Radiometric	Photometric	Radiometric
lx	W.m^-2	Illuminance	Irradiance
cd	W.sr^-1	Intensity	Intensity
cd.m^-2	W.sr^-1.m^-2	Luminance	Radiance
lm	W

The topic presents the different formula of measure calculation considering the following variables:

N = number pixels in the measurement area.
V = value of a pixel.
W = pixel weight.
Pixels on the edges of the measurement area can be partially integrated in the area, hence the formula considers the pixel weight to calculate the selected measure of the pixel part integrated in the area.

Maximum and Minimum

Maximum and Minimum correspond to the Maximum or Minimum of the selected magnitude in the measurement area defined.

These thresholds are used to exclude values in the map (below the Minimum and/or over the Maximum).

It can be useful to ignore black pixels for example. If some pixels are not lit, they introduce a bias into the measurement. A minimum or maximum threshold then allows you to ignore these values.

Average

Average corresponds to the average value of the selected magnitude in the measurement area defined.

Area

To display an area value:

Make sure the shape is a rectangle, an ellipse or a polygon.
In the Magnitude column, select Dimension.

The Measure turns into Area and its value is displayed in the Value column.

Flux or Integral

The flux or integral of the measurement area defined is measured thanks to the following formula:

F (flux) corresponds to the luminous flux in lumen (lm) for an illuminance map.

F (integral) corresponds to the luminous intensity in candela (cd) for a luminance or intensity map.

S = surface (m²) of one pixel for a luminance or illuminance map, or a pixel solid angle in steradian (sr) for an intensity map.

Warning: The computation of the flux assumes that pixels are parallel to the sensor plane. If you tilt the integration direction, it is as if you tilted pixels in the map. Even if the illuminance value at each point of the map is correct, the total flux of sensors having a non-orthogonal integration direction is not reliable.

Note: Flux measurement is not possible on irradiance and 3D irradiance maps that used an Integration type different from Planar (and also an Integration direction that is not perpendicular to the sensor plane).

Barycenter X and Barycenter Y

Note: For intensity maps, the measures are Barycenter Phi and Barycenter Theta.

Barycenter X and Barycenter Y correspond to the X and Y coordinates of the barycenter of the measured magnitude in the measurement area defined.

x (or y) = pixel coordinates on the x or y axis.

Sigma

Sigma corresponds to the standard deviation of the measured magnitude.

Note: Sigma is related to the noise.

= average of the magnitude of the measurement area defined.

Sigma X and Sigma Y

Note: For intensity maps, the measures are Sigma Phi and Sigma Theta.

Sigma X and Sigma Y correspond to the standard deviation according to the barycenter, that is to say the spread on the x and y axes (or on theta and phi).

x (or y) = pixel position on the x or y axis.
B = Barycenter X or Barycenter Y.

Contrast

Contrast corresponds to the scale difference between the maximum and minimum magnitude of the result.

Contrast is generally used to measure the quality of an optical system.


Contrast = 0,58	Contrast = 1

RMS Contrast

RMS (Root Mean Square) Contrast corresponds to the standard deviation of the magnitude measured divided by the average value of the magnitude.

RMS Contrast can be used to measure the noise in the result.

σ = standard deviation of the measured magnitude.

= average of the magnitude of the measurement area defined.


RMS Contrast = 0,39	RMS Contrast= 0,87

The higher the RMS Contrast, the lower the noise.

Range, Range X, Range Y, Range Theta, Range Phi

Note: Range is available for Vertical, Horizontal and User Line.

Warning: Range measures are permitted only with default magnitude and default operator none.

Range corresponds to the distance or angle between Point 1 and Intersection point.
The Intersection point corresponds to the point for which the threshold (iso level) defined is the closest from Point 2.

Range X, Range Y, Range Theta and Range Phi correspond to the coordinates of the Intersection point.


Example of range calculation in an illuminance map with Iso level = 5lx.


Example of range calculation in an intensity map with Iso level = 11cd.

UGR CIE 117-1995

Note: To get the UGR CIE117-1995 measure type, you need to maximize the area and to select the Glare Magnitude first. See how to calculate the UGR value for more detailed information.

The UGR calculation formula is:

Refer to UGR Overview for more detailed information.

Eye Illuminance

Note: Only results coming from a human eye sensor consider the pupil of the eye.

Eye illuminance is the illuminance at the map's observer point due to the light of the map enclosed in the surface tool.

= map normal and virtual eye illuminance sensor's normal. = one direction in the solid angle domain defined by the viewer's surface tool. = map luminance in the direction. = elementary solid angle associated with the direction.