The author visiting Lighthouse (optics) in Kerala, India in 2018.
There are very few people who would not stop by to see, if ever they pass by a Lighthouse. A Lighthouse is one of those few things that has always intrigued us and caught our imagination. Standing by the sea or the ocean, the Lighthouse has stood tall through the test of centuries to help men navigate through the many vagaries of sea life and reach destination safely.
Though the history of Lighthouse can be traced back to the Roman Empire, or beyond, the modern Lighthouse optics is credited to Augustin Jean Fresnel in the 18th Century. Prior to Fresnel, Lighthouse optics consisted of huge lenses that collected the light from an equally big lamp and threw it parallel and collimated many hundred miles over the sea for the ship to navigate. Fresnel understood that much of the refraction done by these huge lenses could be replaced by a thinner lens with a stepped design, each of these steps would bend the light by a certain degree to make the lights emerging from the lamp of the Lighthouse parallel. Thus Fresnel lenses allowed the construction of Lighthouse optics with short focal length and large aperture, without the mass and volume of material that went into prior medieval Lighthouse optics.
Of course, Fresnel lenses were constructed into many types, for the benefit of different types of Lighthouse and their objectives. Thus a Fresnel Lighthouse optics could be of Zero Order ( to throw light to infiniti for ships to see from hundreds of miles away in the ocean ) , First Order to Sixth Orders ( all focusing at a particular distance from the Lighthouse, depending on the need. A sixth order lens would throw light at a shorter distance, specifically placed near harbor.
The modern day diffractive multifocal lenses are a concept from Fresnel Lenses. As you are aware, these lenses are stepped or saw tooth designed to create multiple focal points. The Fresnel lenses applied in diffractive multifocal lenses is to collect parallel rays and focus it on the retina. In the Lighthouse, it is however the other way round , where the light is collected from the lamp, and thrown parallel to the sea. The basic optics however remains the same.
The Fresnel optics together with Thomas Young’s Diffractive Interference of Light have helped create the modern diffractive multifocal lenses. Young’s interpretation of the wave theory of light showed the world how light could be played with, to create constructive interference and thus “orders” or focal points. Ophthalmic scientists are heavily indebted to Fresnel and Young, for their contribution to optics and paving the way for modern diffractive multifocal lenses.
Young’s Double Slit Experiment :
Thomas Young took forward Hyugen’s principle on wave theory. Hyugen stated that every point on the wavefront is in itself a source of secondary wavelets, the sum of all wavelets together forming the waves.
So light travels in waves ? Not in straight lines ? To this debate then in the 18th century, Thomas Young brought to an end with his now famous Young’s Double Slit Experiment.
In Young’s double slit experiment, the science on which all diffractive multifocal IOL is based, light is passed through the first (single slit) on the left of the image on Fig 1. The light that passes through the slit spreads as it comes out of the opening. This spreading of light, as light passes through the slit is called diffraction. The spreading of light through the slit or opening is inversely proportional to the opening in the slit, that is, the larger the slit the less spread out the light is. Or less the opening of the slit, the more the spread out of the light as it passes through the opening. When you look at the optics of any diffractive IOL (fig 4), you can relate the steps or rings on its optics as slits or openings which help light to diffract and fall at a particular focal point. If you look at the optics more closely, the distance between the steps are not uniform. The distance between the steps decreases as you move from the centre to the periphery of the diffractive optics. This is because, as you move away from the centre, you will have to bend the light more, inorder to make it fall on the focal point. This is the simple rule of diffraction.
Coming back to Young’s double slit experiment in fig 1, the light that passes through the first slit now spreads out and then passes through two slits kept at a little distance away. As the light waves passes through these two parallel slits, they in turn form two separate wavefronts. These wavefronts would now interact with each other and ultimately fall on a screen that is placed at a few metres away from the second pair of slits. You will find alternate bands of bright and dark spots on the screen. The bright spot (maxima) that is exactly at the centre of the two slits is of maximum brightness and is called 0 order. As you move from the zero order, all subsequent bright spots will be of diminishing intensity (see fig 2). If you have to relate it to modern day diffractive IOL, the focal point that receives light from the central bull’s eye or the centre of the diffractive steps, is the dominant focal point and is often the distance focal point or zero order of the lens.
Keeping our focus on Young’s double slit experiment, if you look at fig 2 , you will see a number of bright and dark spots. The bright and dark spots are the result of crests (high) and trough (low) interacting with each other as they come out of the two slits. This is the law of interference of light. As the crest of one wave emerging from one slit, meets the crest of another wave emerging from the second slit, a bigger wave is created - the result of which is seen as several bright spots on the screen. On the corollary, as the trough of one wave meets the crest of the other wave, dark spots are seen on the screen. You can relate this to the waves of the sea, wherein the high/crest of one wave meeting the low/trough of the other results in a negation of the waves, while the high/crest of one wave meeting the high/crest of another wave results in a bigger wave formation.
Relating this to the science of diffractive IOLs, it is always desirable to utilize as much light as possible all directed at the two focal points of a bifocal IOL. This can be only achieved, when the crest meets the crest of the wavefronts of light passing through the diffractive IOL optics. That being said, some light loss is inevitable as the crest of one wave meets the trough of the other.
The question here is that, how can we space the steps/rings of the diffractive IOL in such a way that all light passing through the diffractive optics falls on the two focal points of a bifocal IOL ? At what distance should these steps be spaced to each other to utilize the maximum light waves for the focal points ? Herein comes the importance of understanding wavelengths, and its importance in diffractive IOLs.
Wavelengths
Wavelength (λ) is the distance between the crest of one wave to the other, or the trough of one wave to the other. Or in simple words, wavelength (λ) is the completion of a cycle from one wave to the other. We have discussed before, that the bright spots on the screen are created when the crest of one wave meets the crest of the other wave. When does the crest/trough of one wave meet the crest/trough of the other wave so that a bright spot is created? The answer is the crest of waves travelling from one slit will meet the crest of waves emerging from another slit only when the difference in the distance travelled in terms of wavelength is an integer of 1, that is 1λ, 2λ, 3λ, etc. If the difference in wavelength travel between two waves emerging from the slit is not an integer of 1, a destructive interference is created, and dark spots or faint bright spots will be created.
Again, to relate this aspect to diffractive IOL science, all step/ ring boundaries are created in such a way that waves emanating from each successive steps have a difference of 1λ. In Figure 3, two waves are emerging from slits A and B. The slit B is placed from slit A at such distance, so that the difference in wavelength between the waves emerging from both slits is 1λ. Let BP be the distance covered by the wave emanating from slit B. The extra distance that this wave travels to meet the wave AP at the point P is BD. In mathematical terms, BD is 1λ.
More explanation to Fig 3 for enthusiasts:
At what distance should the slits (openings) be placed so that BP is 1λ more than AP. To derive this distance, consider a drawing a straight line AD such that BD is perpendicular to AD. The distance BD is the extra distance travelled by the wave to meet the wave AP at point P. Since BD is perpendicular or at right angle to AD,
sinθ=P/H or sinθ= BD/AB or sinθ= s/d , or s = dsinθ, where d is the distance between each slit, and s is the difference in path length between two waves emerging from the two slits and converging at point P. If s is the path length difference, then we can re write the formula as dsinθ= mλ where m is the integer of wavelengths depending on the slits positioned in the experiment
That is, the slits in Young’s double slit experiment is placed in such a way, that the distance d between two slits follows this rule. Only then will the crest of one wave emerging from one step meet the crest of another step leading to a bright light or maxima.
Again, applying this basic science to the world of diffractive IOLs, the successive steps in the diffractive optics are arranged in such a manner, that waves travelling through these steps all meet at the focal points, that is the distance travelled by the waves are an integer of 1λ. Each step boundary is place immediately when the distance travelled by one wave is more than 1λ of the other wave. In this way, the step distances ensure that all light are focussed to the two focal points of a bifocal IOL. As stated earlier, as the steps move from the centre to the periphery, the distance between the steps come down. This is because, by the law of diffraction, the opening between two steps need to be reduced to help peripheral ray of light be bend more to converge on the focal points.
More on the Steps/ Rings of Diffractive IOLs:
As light comes from the air and enters the IOL ( in the eye replace air with aqueous ), the light that passes through the base curvature of the IOL ( refractive part ) bends and falls on the distance focal point. As light passes through the steps, light diffracts. As this light diffracts on hitting the steps, the light reach the zero order (distance), the first order (near) for a bifocal IOL. Ofcourse the light does not only reach the two orders but also other higher orders. The light that reach second, third, or other higher orders are considered to be the light lost.
Height of Steps:
The height of the steps or rings helps in the distribution of incoming light into distance and near focal points. The greater the height of the steps, more the incoming rays of light are directed to the near focal point by creating a greater phase delay.
Keeping other things constant, the step heights are a function of the percentage of light desired to be focussed on the near focal point, the wavelength of (monochromatic) light experimented with and the refractive indices of the IOL and the medium , where h is the height , α is the percentage of light desired to be focussed.
Contrary to the popular belief that diffractive IOLs can only be designed to provide multifocality, such IOLs may at least theoretically be designed as monofocal optic. Chose the value of α as 1, and you will get all light directed to only one focal point.
Diameter of the Bull's eye, or the center of the diffractive steps or rings:
The light that passes through the central bull's eye of the innermost diffractive ring may pass to the distance or intermediate focal point. For the ReSTOR +4, this light reached the distance focal point but for the trifocal IOL PanOptix (Alcon), the light reaches the intermediate focal point.
It has been commonly known that the higher the central radius of the diffractive profile, the more forgiving is the diffractive multifocal IOL to decentration. It has been often pointed out that the radius of the centre of diffractive element should be no less than the chord mu or chord alpha of the patient.
The centre of the diffractive element cannot be increased arbitrarily. It's width is determined by the add power that is designed in the bifocal or trifocal diffractive lens. The add power is adjusted by varying the width of the diffractive steps or rings. As the zone width is increased the add power is decreased (6). The equation that governs this relation is :
Where i is the step or ring number, λ is the design wavelenth of light, Dadd is the add power of the lens, r is the radius of the ring/step. Thus if you are calculating the diameter of the first diffractive ring, the value of (2i-1) is 1. Therefore the equation stands as λ*1000/add.
Taking the Restor +4 add power lens the radius will be .375 mm. Here are the steps to calculate
convert wavelenth of light to mm : 550 nm of light is equal to .00055 mm.
Convert add power to mm :4D =25 cm = 250 mm ( 1D = 1000mm)
Multiply .00055 with 250 mm and take the root of the product
therefore r is .37. Diameter will be 2 times the radius .741
Remember the value of this diameter will change if the wavelenth of light is changed. Conceptual only.
Let us do this for the ReSTOR +2.5 and PanOptix taking wavelength of light 550 nm (conceptual only).
ReSTOR +2.5 with 550 nm of light
Convert wavelenth of light to mm : 550 nm of light is equal to .00055 mm
Convert add power to mm : 2.5 D = 40 cm = 400 mm (1D = 1000 mm)
Multiply .00055 with 400 mm and take the root of the product
Therefore r is .469. Diameter will be 2 times the radius .938mm (conceptual only)
Calculating the diameter of the bull's eye zone of trifocal IOLs that dedicate light to the intermediate (not distance):
The central bull's eye zone of PanOptix is said to be approximately 1.164 mm (9). The PanOptix dedicates light through this region to the intermediate and not the distance. How will the above calculation of the bull's eye be worked upon. For the enthusiasts, below is the calculation of how you can arrive at the bull's eye diameter of the PanOptix or any trifocal IOL that has the central bull's eye dedicated to intermediate.
· Example: PanOptix bull’s eye is dedicated to intermediate.
· The near add power of PanOptix is 3.25 dioptre. Take half of 3.25 dioptre 3.25/2= 1.625 dioptre (this could be the power of the intermediate zone in PanOptix)
· Convert the 1.625 dioptre add power to mm: 615.38 mm.
· Convert the wavelength of light to mm: .00055 mm (assuming a 550 nm of wavelength is used)
· Multiply .00055 as wavelength of light with focal length of 615.38 and take the root = .581 mm
Therefore, radius of PanOptix is .581 mm. Diameter is two times the radius, 1.16
Side by side comparison of the bull's eye central diameter of Panoptix with the Symphony. Source: Review of optometry, Dec 15, 2020. Image Aaron Bronner, MD
If you are interested in knowing the diamter of the central diffractive ring or bull's eye, you can use my calculator here to understand approximately the size:
Thus, since the add power of the lens is directly linked to the diameter of the bull's eye, a careful choice has to be made between the two. Lenses like the Symphony (J&J) have a very high bull's eye, at the cost of a very low add power (the Symphony was marketed as an EDOF lens), while the ReSTOR +4 had a lower bull's eye (.7mm) as its add power was high. Between the two lenses is the ReSTOR +2.5 with a central bull's eye of .938mm.
In conclusion:
Diffractive optics providing multifocality has come a long way ever since its first inception decades ago. Companies continue to innovate to provide a better near, intermediate and distance vision to patients. However, in optics, there is no free lunch. The law of diffraction, science of wave propagation and diffractive interference, puts significant limitation to what can be achieved and be relatively acceptable to patients without significant compromises. Patient selection and counselling will remain the two most important aspects on which surgeons and doctors will have to depend on to create a pool of happy patients.
June, 2021
Kolkata, India.