The effect of telescope aperture, scattered light and human vision on early measurements of sunspot and group numbers

Early telescopic observations of sunspots were conducted with instruments of relatively small aperture. These instruments also suffered from a higher level of scattered light, and the human eye served as a 'detector'. The eye's ability to resolve small details depends on image contrast, and on average intensity variations smaller than approximate to 3 per cent contrast relative to background are not detected even if they are resolved by the telescope. Here we study the effect of these three parameters (telescope aperture, scattered light and detection threshold of human vision) on sunspot number, group number and area of sunspots. As an 'ideal' dataset, we employ white-light (pseudo-continuum) observations from the Helioseistnic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory, and we model the appearance of sunspots by degrading the HMI images to corresponding telescope apertures with added scattered light. We discuss the effects of different parameters on sunspot counts and derive functional dependences, which could be used to normalize historical observations of sunspot counts to a common denominator.