Context. Recently, a possible identification of type II spicules in broad-band (full-width at half-maximum (FWHM) of ~0.3 nm) filter imaging data in Ca ii H on the solar disc was reported. Aims: We estimate the formation height range contributing to broad-band and narrow-band filter imaging data in Ca ii H to investigate whether spicules can be detected in such observations at the centre of the solar disc. Methods: We applied spectral filters of FWHMs from 0.03 nm to 1 nm to observed Ca ii H line profiles to simulate Ca imaging data. We used observations across the limb to estimate the relative intensity contributions of off-limb and on-disc structures. We compared the synthetic Ca filter imaging data with intensity maps of Ca spectra at different wavelengths and temperature maps at different optical depths obtained by an inversion of these spectra. In addition, we determined the intensity response function for the wavelengths covered by the filters of different FWHM. Results: In broad-band (FWHM = 0.3 nm) Ca imaging data, the intensity emitted off the solar limb is about 5% of the intensity at disc centre. For a 0.3-nm-wide filter centred at the Ca ii H line core, up to about one third of the off-limb intensity comes from emission in Hɛ. On the disc, only about 10 to 15% of the intensity transmitted through a broad-band filter comes from the line-core region between the H1 minima (396.824 to 396.874 nm). No traces of elongated fibrillar structures are visible in the synthetic Ca broad-band imaging data at disc centre, in contrast to the line-core images of the Ca spectra. The intensity-weighted response function for a 0.3-nm-wide filter centred at the Ca ii H line core peaks at about log τ ~ -2 (z ~ 200 km). Relative contributions from atmospheric layers above 800 km are about 10%. The inversion results suggest that the slightly enhanced emission around the photospheric magnetic network in broad-band Ca imaging data is caused by a thermal canopy at a height of about 600 km. Conclusions: Broad-band (~0.3 nm) Ca ii H imaging data do not trace upper chromospheric structures such as spicules in observations at the solar disc because of the too small relative contribution of the line core to the total wavelength-integrated filter intensity. The faint haze around network elements in broad-band Ca imaging observations at disc centre presumably traces thermal canopies in the vicinity of magnetic flux concentrations instead. Appendix A is available in electronic form at http://www.aanda.org