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A multifunctional setup based on the absolute integrating sphere method for measuring luminous flux of light emitting diodes (LEDs) is presented. The total luminous flux in 2π and 4π geometries and partial luminous flux with variable cone angle can be measured with the same custom-made integrating sphere. The number and area of ports and baffles of the sphere was minimized. The sphere has three ports: a main port, a detector port, and an auxiliary port, located in the same hemisphere. The other hemisphere is free of ports. The main port is used for the calibration of the sphere as well as for the LED under test. Only one absolute calibration of the integrating sphere photometer is needed for measuring LEDs in all three geometries. The spatial nonuniformity correction is needed only for LEDs with low directivity or having significant minor beams. The expanded uncertainty (k=2) for the measurement setup varies between 1.2% and 4.6% depending on the measurement geometry, color, and the angular spread of the LED light beam. A complete calibration procedure of the constructed integrating sphere photometer is presented as well as comparison measurements with a goniophotometer. [ABSTRACT FROM AUTHOR]