Measuring portal dose with an electronic portal imaging device (EPID) in external beam radiotherapy can be used to perform routine dosimetric quality control checks on linear accelerators and to verify treatments ( in vivo dosimetry). An accurate method to measure portal dose images (PDIs) with a commercially available fluoroscopic EPID has been developed. The method accounts for (i) the optical `cross talk' within the EPID structure, (ii) the spatially non-uniform EPID response and (iii) the nonlinearity of the EPID response. The method is based on a deconvolution algorithm. Measurement of the required input data is straightforward. The observed nonlinearity of the EPID response was largely due to the somewhat outdated EPID electronics. Nonlinearity corrections for more modern systems are expected to be smaller. The accuracy of the method was assessed by comparing PDIs measured with the EPID with PDIs measured with a scanning ionization chamber in a miniphantom, located at the same position as the fluorescent screen. For irradiations in open, wedged and intensity modulated 25 MV photon beams (produced with dynamic multileaf collimation) EPID and ionization chamber measurements agreed to within 1% (1 SD).