1. A fluorescence observation apparatus comprising: an illumination section that includes a light source for irradiating a subject with illumination light and excitation light; a fluorescence image acquisition section that acquires a fluorescence image from fluorescence produced in the subject irradiated with the excitation light emitted from the illumination section; a return-light image acquisition section that acquires a reference image from return light returning from the subject irradiated with the illumination light emitted from the illumination section; an exposure-time adjustment section that adjusts exposure time based on a luminance value of the reference image acquired by the return-light image acquisition section; an illumination control section that controls the intensity of at least one of the illumination light and the excitation light emitted from the illumination section, based on the exposure time adjusted by the exposure-time adjustment section; first normalization section that normalizes the luminance of at least one of the reference image and the fluorescence image by the exposure time; second normalization section that normalizes the luminance of the at least one of the reference image and the fluorescence image by the intensity of the at least one of the illumination light and the excitation light controlled by the illumination control section; and an image correction section corrects the fluorescence image by the reference image, by using at least one of the reference image or the fluorescence image normalized by the first normalization section and the second normalization section.