Conical light distribution of lamps and lanterns USES illumination calculation lumen output method discussed in this paper

Illumination of fixed distance compare has been more widely as a two lamps and lanterns is one of the simple and effective method of brightness, then, have slightly difference of Angle for the lamps and lanterns, comparison of the axial intensity of illumination and cannot explain the difference of lumen output. The lamps and lanterns of 15 degrees, for example, the axial 100 lx, axial 90 lx, the lamps and lanterns of 20 degrees which a lamp high lumen output? Makes for the general owners and designers, it is not easy, test a lamps and lanterns IES costs are not low, time is long.

the illuminance data again a little bit more actually, we like integrating sphere can be concluded that the number of lumens of lamps and lanterns, especially with conical light distribution, smooth transition of the lamps and lanterns and light distribution curve is the most simple, this paper introduces a simple light distribution on the number of lumens.

this type of light source conical light distribution meet the following conditions as the approximate point light source, a light distribution to 120 degrees ( 50% of the beam Angle) Lambertain light distribution, chip as the rectangle, approximation for point, the secondary light distribution lens surface to grind arenaceous, or cellular level best, smooth surface can approximate treatment, intensity of illumination in line with the inverse square of the distance attenuation.

general cone with light beam Angle and the flare Angle two Angle parameters, beam Angle by 50% light intensity in the line of Angle, the axial section of flare Angle by 10% light intensity in the line of Angle, the axial cross section of average about 2 times of the latter to the former.

statistics of the proposed method is of all flare Angle corresponding to the range of lumen, namely all lumens count within 10% light intensity.

this method is based on the principle of the lumen is by intensity of illumination and area. Lumens on a small enough area is the area of illumination and the total area of the product, so the spot of the lumen is there in all directions on the intensity of illumination in the area of integral, considering the light spot is round, circle direction illumination approximately equal, can be calculated as the direction of the intensity of illumination in the length of the radius on the micro rings on the integral, in order to establish the coordinate system XOZ (more clearly shown as follows, Used here Z is only as a function of subsequent reference staggered, not involving the 3 d coordinate) , O for spot center.

• generally identified as light illumination strongest points coincide with the center of the circle point O

• testing on the same radius of circle y is almost the same intensity of illumination,

in any position, the intensity of illumination is a function of x, y after test for gaussian fitting that

intensity of illumination acquisition methods, is suitable for the axial distance to light lamps and lanterns, formed perpendicular to the axial spot

, try to adjust to there, at the same distance from the center of illuminance is the same or close to

• to flare in the grid, at least 11 * 11 = 121 point grid array, the thinner the better

• gathering point of the grid must cover all areas within 10% light intensity, can a few points from the 10% light intensity distribution, can also be used for calculating and fitting, less effect on the results. The integral reasoning process

select a radius of x in circle, thickness is very thin, for an infinitesimal increment dx, then the circle area of 2 * 3. 1416 x * dx, the circle in the intensity of illumination to y, the rings on the lumen is ( 2 * 3. 1416 x * dx) * ( y) , on the spot within the effective radius of distance to definite integral, the numerical integral threshold is 0, integral upper limit of 10% light corresponding to the length of the radius r,

data processing will be collected numerical, center symmetrical averaged four points, as the illumination of the coordinates at that point, The link can further reduce the system error) Data, and then use the Origin software to center distance of illumination 'distance' mapping, and gaussian fitting, get the standards and the fitting formula:

there are constant y0, xc, w, A, in addition, x is the distance from point O, y to x distance of illuminance, * 3 to 2. 1416 x * y * dx for lumen numerical integral or get requirements.

which is suitable for spot radius r, as the integral upper limit of the definite integral, the need to use compound derivation formula ( eu( x) ) '=eu( x) ∙u( x) 'that can calculate the accurate value.

for example, suppose a projected on the walls of lamps and lanterns is 2 meters radius of light, after data collection and fitting, get the

to

of composite derivation formula (u derivative use eu( x) ) '=eu( x) ∙u( x) ',

it

so, the original score = 462. 62 + 4851. 7×0. 0308 = 612

the lumens of lamps and lanterns * 3 = 2. 1416 * 612 = 3845 lm。

is evaluated.

this method, we propose the use of the intensity of illumination calculation for lumen fit without the large equipment, integrating sphere and dark room on the number of cases are used to calculate the lumens of lamps and lanterns, especially the comparison of a large and small Angle axial light intensity and large Angle is small when the axial light intensity of the lumen output of lamps and lanterns is very nice, suitable for use in identifying and purchasing products, can also be used to evaluate the light field test for the lamps and lanterns.

author introduction

Han Baiguang

guangzhou longman photoelectric technical director, global design support center chief designer

the national senior scholars association of lighting designers, Chinese CLDA professional lighting designers association, member of IALD Affiliate member of lighting designers association of North America.

China lighting network original author Han Baiguang