matter how we digitally zoom the image. For the iPhone 6s, this happens at a distance of 7.5 feet or
2286 millimeters. So again from the above formula we now have w=1 millimeter and d = 2286
millimeters so the half-angle is 0.0125
o
and the resolution is 0.025
o
. Now, astronomers tend to use
arcseconds as a unit of angular measure because most astronomical objects are pretty small in the sky,
so this becomes an angle of 0.025x3600 = 90 arcseconds, or alternatively 1.5 arcminutes. Now the
resolution of the human eye is about 1 arcminute in the middle of the visible spectrum, so this camera
will show a scene at slightly worse than ‘retinal’ resolution. For example, at a distance of 7.5 feet, a
normal human eye would have seen the markings in the meter stick above with a ‘bit’ more clarity. This
difference, outdoors, is not discernable by most people given the varying responses of the human pupil
to changing light conditions. It is the available, full diameter of the human eye pupil (larger at night and
smaller in the day) that determines your visual acuity.
So what does this demonstration have to do with eclipse photography? For astronomical
purposes, the most important factor in any imaging system, be it a telescope or a camera, is its ability to
resolve details in the objects being studied. Because objects in the sky are measured in terms of angular
units, we have to figure out how well our imaging system can resolve details at a specific angular scale.
The basic formula that determines the angular subtence of an object is = 206265 diameter/distance,
where the diameter and distance are in the same units ( meters, kilometers, light years) and the
calculated angle, , will be in arcseconds. Recall that there are 360-degrees in a full circle. Each degree
can be divided into 60 arcminutes, and each arcminute can be divided into 60 arcseconds and 1 radian is
an angular measure equal to 206,265 arcseconds. (360 degrees/2 = 1 radian = 57.2958 degrees x 3600
= 206,265 arcseconds). During the August 21, 2017 total solar eclipse, the diameter of the sun and moon
are both 1897 arcseconds or just over 0.5 degrees.
What this means is that for our example of the iPhone 6s at its native 1x resolution, its 90
arcsecond resolution will cover the diameter of the sun and moon by 1897/90 = 21 resolution elements.
That is the best you will be able to do no matter what ‘photoshop’ trickery you try to do! The way in
which a smartphone’s pixels are matched to its maximum optical resolution is actually complicated by
the fact that the pixels in the very small CMOS chip are greatly magnified so that they can be displayed
on the screen of the smartphone. Manufacturers talk about ‘retinal resolution’ for their displays but this
has little to do with the actual optical resolution of the CMOS sensor! The iPhone 6s boasts a retinal
resolution, but as we have seen, the camera resolution itself is about 50% worse than the canonical
definition of typical human retinal acuity.
The only way to optically improve the clarity of an image is with the smartphone attached to a
telephoto, a pair of binoculars or a telescope. This makes the aperture of the camera lens much larger,
and so it decreases the angular scale of the field of view, which is covered by the CMOS array pixels.
I purchased what was advertised as a 12x telephoto lens for an iPhone 6s to see how much
improvement I would get. This, by the way, is not really suitable for hand-held operation. The lens clips
on to the iPhone over the existing camera lens, but this attachment is very fickle and subject to slippage.
You have to remove the iPhone case completely, and through considerable trial and error find the
optical sweet-spot where the optical axis of the telephoto lens is aligned with the camera’s optical axis.