TL;DR: My approach was to use the fact that I personally went through "vision therapy" to identify a similar exercise to what the question describes (one which alternates between extreme divergence (looking far away) and convergence (focusing up close)). This allows us to examine the literature for the field of vision therapy for determinations of efficacy. I used sources to confirm my descriptions/experience.
Then I took a look at the available literature for the field of vision therapy:
There does not appear to be any scientific support for vision therapy in terms of improving visual acuity and/or reducing myopia (nearsightedness).
I'm using "improving eyesight" to mean increasing acuity (require lower prescription glasses or no glasses), which also entails reducing farsightedness.
As shown in the sources section, there may be improved farsightedness, as the literature indicates that convergence exercises have some benefit. Improving the ability of the eyes to converge and bring something into focus up close would, indeed, have the potential to assist those with trouble seeing up close. The literature simply mentions that convergence is improved, but didn't specify on whether that translated into a reduction in hyperopia (farsightedness, which probably requires reading glasses for seeing up close).
This would fall under the umbrella of "Behavioral Vision Therapy," something I went through as a child for several years. Wiki has an article about it HERE, and there is a link there from the General Research section of the Bates Method page (LINK), so I think the two are at least somewhat similar in their approach.
The exercises involve several techniques (this is from personal involvement in this method, though many more are listed on the Wiki page):
- brock strings
- balancing (see picture of girl on balancing board) while looking at a hart chart or marsden ball
- tossing bean bags at something like THIS and catching them with alternating hands or spinning around between throwing and catching
There are many other methods, such as using prismatic glasses, 3D images and trying to get it to "pop" or "recess" (based on whether you are converging or diverging your eyes); many of these techniques are shown HERE in this blog post (used this site because it contained the most helpful/various pictures in one place).
Your specific exercise
What you are describing sounds like a variation on a convergence/divergence exercise. In particular, I used one of THESE lifesaver cards. They are clear or opaque; with the clear cards, one stands in front of a window and looks through the card toward something very far away and as a result, the red and green lifesavers will come together and form a 3D image. One gets them to "lock," (verified by reading the letters on the lifesaver), holds, and then converges (crossing eyes -- same as looking at something very close) to form a 3D image from the red and green images.
This is the same phenomenon as magic eye images. When one changes the point of focus to a point behind or in front of the image, the images from the left and right eye will superimpose upon one another and form a new, composite image, which appears to be 3D if different features are present in each of the respective images.
See THIS video instruction for using lifesaver cards as a validation of my explanation. The video is from a Behavioral Optometrist, shown by the FCOVD after the name (Fellow in the College of Optometrists in Vision Development).
I'm using my past experience and participation in vision therapy, combined with illustrating that this particular exercise seems to perform the same mechanics (focusing up close, then looking far away) to find a "field" one can examine for efficacy. With just the description alone, it may have been tough to figure out of such a method has been tested, but, if we can pin the words "vision therapy" to it... we have a much better base in the available literature.
- Helveston, "Visual training: current status in ophthalmology," 2005 (LINK)
Most visual training is now done by optometrists and others who say it works. Based on an assessment of claims and a study of published data, the consensus of ophthalmologists regarding visual training is that, except for near point of convergence exercises, visual training lacks documented evidence of effectiveness.
An example of "near point convergence exercises" are "pencil push-ups," shown HERE, is the practice of taking a small object and moving it closely toward the nose. The patient tries to focus on it as it approaches; if/when the eyes cannot maintain the convergence, two images will form. This is not the same as alternating between extreme convergence and extreme divergence in order to improve vision. This is to assist those who have trouble focusing up close and tracking movement.
- Rawstron, "A systematic review of the applicability and efficacy of eye exercises," 2005 (LINK)
Forty-three refereed studies were obtained. Of these, 14 were clinical trials (10 controlled studies), 18 review articles, 2 historical articles, 1 case report, 6 editorials or letters, and 2 position statements from professional colleges. Many of the references listed by the larger reviews were unpublished or published in obscure or nonrefereed sources and therefore were not accessible. Conclusions: Eye exercises have been purported to improve a wide range of conditions including vergence problems, ocular motility disorders, accommodative dysfunction, amblyopia, learning disabilities, dyslexia, asthenopia, myopia, motion sickness, sports performance, stereopsis, visual field defects, visual acuity, and general well-being. Small controlled trials and a large number of cases support the treatment of convergence insufficiency. Less robust, but believable, evidence indicates visual training may be useful in developing fine stereoscopic skills and improving visual field remnants after brain damage. As yet there is no clear scientific evidence published in the mainstream literature supporting the use of eye exercises in the remainder of the areas reviewed, and their use therefore remains controversial.
So, again we have support for convergence insufficiency (mentioned above), some evidence indicating that regaining depth perception (stereoscopic skills) after brain injury is supported... but overall, nothing supporting the use in other areas (such as improvements in "visual acuity" -- what we typically mean when we say "better vision").
- Barrett, "A critical evaluation of the evidence supporting the practice of behavioural vision therapy," 2008 (LINK)
Although there are areas where the available evidence is consistent with claims made by behavioural optometrists (most notably in relation to the treatment of convergence insufficiency, the use of yoked prisms in neurological patients, and in vision rehabilitation after brain disease/injury), a large majority of behavioural management approaches are not evidence-based, and thus cannot be advocated.
If you read the previous text, this study examined the efficacy for reducing myopia (nearsightedness, which requires glasses to see things at a distance), which I'll group in the "better vision" category.
As I stated in the intro, these sources do mention convergence improvement techniques may be valid, but I'm not sure how that translates into practical details -- are reading glasses prescriptions able to be reduced, for example?
In any case, convergence exercises is not what you're describing here, and so it's somewhat irrelevant. You are describing an alternating convergence/divergence exercise, and it does not appear to be supported by the literature.