A modified design of a CaF2/acetone bandpass photon detector that uses Kr as a filter gas to tune the energy resolution is presented. Our design combines two standard single window detector tubes to build the Kr filter gas chamber. Synchrotron radiation has been used to determine the energy resolution of the detector, as a function of Kr pressure. The improvement in the detector energy resolution by 250 meV compared to the CaF2/acetone detector is better than that reported earlier. Substantial variation in the shape of the CaF2/acetone detector response functions is observed for different acetone pressure (≤3 mbar), and anode voltage (≤800 V). Our analysis reveals that the changes in the shape of the detector response function are associated to different regions of the detector operation.