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Reflector Synthesis

SHAPE's distinctive feature, in comparison with similar reflector design programs, is the calculation of reflector shape coordinates according to the specified light source characteristics and the illuminated area. The reflector design initial data should be regarded as illuminance on the working plane or a luminous intensity distribution of the optical system (a lighting device). Such a method of reflector design (from the specified light distribution to the reflector shape) reduces prototyping costs and raises energy efficiency of a lighting device.

SHAPE provides control of reflector synthesis by checking calculation which recalculates the light distribution from the newly built reflector shape. The optical system parameters may be imported into the reflector design project where it is possible to estimate the system stability against defocusing and aberrations.

Problem Description

Input ParameterValue
Rotational, Cylindrical
Rotational SymmetryCylindrical Symmetry
Rotational SymmetryCylindrical Symmetry

Light Source

Input ParameterValue
Type of source
Point, Line (only Cylindrical Symmetry)
Luminous intensity distribution
I(α) – discrete array of points
Type of the curve interpolation
Linear, Spline

Luminous intensity distribution of the light source – I(α), cd/klm

Luminous intensity distribution of the light source 

Note: During the calculation of the luminous intensity distribution curve is normalized to a flux 1000 lm.


Input ParameterValue
Start angle
Final angle
Initial radius
Number of calculation points
N, Auto Fit

Various combinations of starting and final angles are supported in the program.

Rotational Symmetry

Rotational SymmetryRotational Symmetry

Cylindrical Symmetry

Cylindrical SymmetryCylindrical Symmetry

Output Data

After calculating the shape array appears in the following forms:

  • in Cartesian coordinates: Z(x)
  • in polar coordinates: R(α)
  • Ray-tracing function (dependence between incident and reflected rays): α(γ)

Illuminated Area

Input ParameterValue
Direct light from the source
On, Off
Type of light distribution
Luminous intensity distribution curve, Illuminance
Luminous intensity distribution
                Luminous intensity distribution
I(α) – discrete array of points
                Boundary angular coordinates
αs ÷ αf
Illuminance distribution
                Illuminance distribution
E(x) – discrete array of points
                Distance to the working plane
                Boundary linear coordinates
Xs ÷ Xf   

There is a dependency between boundary rays and boundary coordinates of the illuminated area. Thus, straight or crossed schemes of ray-tracing can be used. 

Divergent scheme of ray-tracingConvergent scheme of ray-tracing
Straight scheme of ray-tracingCrossed scheme of ray-tracing

Light source luminous intensity distribution – I(α), cd/klm

Luminous intensity distribution

Illuminance distribution – E(x), lx/klm

Illuminance distribution