Decoding : Anti-Reflective Coating

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Anti-reflective coating aka ARC is an external layer created by particles of metal oxides in form of very thin sheets over the surface of the ophthalmic lens which could be applied both to front and back of the lens. Anti-Reflective coating is applied either in form of a single layer or multiple layers of coatings which is called as anti-reflective stack. Various other treatments like hydrophobic, oleophobic and anti-static are added over the pre applied anti-reflective coating. UV absorbing coating is also sandwiched in between of these coatings to prevent from UV A&B. Main purpose of Anti-Reflective coating is to reduce the number of reflected rays without any loss in the light energy as that energy gets converted in the transmitted energy hence increasing the amount of transmission through an ophthalmic lens so that there is minimum loss of brightness and contrast of the image being formed by the lens.

Image 1 when being viewed with non coated lens Image 2 when being viewed with arc lens

What is reflection and what causes it-:

Whenever light rays fall on a transparent surface, in this case our ophthalmic lens they undergo multiple phenomena of which primary ones are Reflection and Refraction. Reflection is the bouncing back of the light rays into the same plane from which the light rays were coming but in a different direction and Refraction is the transmission of light rays through lens but with change in its original direction. Both of these things take place due to the sudden change in the medium of the light ray path which deliberately make the light ray’s particle to change the nature of orientation. In case of ophthalmic lenses this change of medium takes place at two junctions first one being the front surface of lens at which light travels from air into the lens and the second junction is the back surface where light travels from lens into the air. Both reflection and refraction take place at these two junctions and the reflected rays from both the surface adds up by the phenomena of constructive interference and thus increase the reflection. This phenomenon is what that makes the basis of Anti-Reflecting coating which makes the reflected rays of front and back surface to cancel out each other.

Factors affecting the amount of reflection-:

1. The angle of incidence :- When light rays are parallel to the plane of lens minimum reflection takes place but as the angle increase from 0 to 50 the amount of reflection increases but still is very less but as the angle increases further from 50 to 90 sudden increase in reflection takes place being maximum when the light rays are perpendicular to the lens surface.

2. Distance between the source of light and the lens surface:- As the distance decreases the reflectance flux (luminosity of light flux reflected/Luminosity of light falling on surface) increases hence the reflection increases in addition as the size of light source increases keeping the intensity same reflection decreases.

3. Refractive index of the lens:- which is explained by the formula of reflectance i.e., (RI of Lens-RI of air/RI of Lens+ RI of air)sq which states that as the Index of lens increases amount of reflectance increases which also becomes the reason for commercially available hi-index lenses to be AR coated by default.

4. Thickness of the lens:- rings being present at the edge of a high-powered minus lens and for a positive lens as the power increases the centre thickness increases thus the reflection increases. When assessing the front surface of a plus and a minus lens it could be clearly seen that a plus power lens will have more reflection then observed in the minus power lens of same power.

How reflection troubles the wearer-:

Reflection from lens surface is experienced in several manner both by the observer and the wearer. Reflected images are both virtual one and real one kind of images. Real images are termed as Ghost images and are formed by both front and back surfaces of the lens on which light rays are incident both from front and back of the lens. A total of 5 ghost images are typically formed.

Ghost image 1 which is the most significant and having an intensity of about 0.15% for a lens of Refractive Index 1.50 which increases to 0.17% for a lens of index 1.523 and for a much higher index like 1.70 its intensity is around 0.39%. It is seen as a second image of the light source which is more prominently seen while viewing a bright light source in dim illumination or night time For example while viewing a street light or car’s headlight a second image which is fainter than the original light source is observed. It is formed due to double internal reflection taking place at both front and back surface of the lens. Vergence of Ghost image is given by L’= L1(incident vergence+(3n-1/n-1)F (vergence of lens). To make ghost image into sharp focus and at the subject’s far vergence of ghost image should be equal to the vergence of lens used so that both images are focused at same point which would generally be the subject’s far point, which is only possible for extremely low power with maximum amount to be around 0.20D for lens of refractive index 1.90 otherwise for majority of conditions the ghost image is out of focus. Ghost images are seen always closer than the object’s position in space. Prismatic effect could also add up to the formation of ghost image and images would never be superimposed even when lying on the optical axis of the lens.

Ghost image 2 is formed due to reflection at the cornea and back surface of the lens. Vergence of ghost image is dependent on the vertex distance and the back surface power of the lens. L’= -Z(vergence of Purkinje Image 1)+ -2F2/n-1. It has been found by using various number of powers that to superimpose ghost images i.e., to make L’=F lower the minus power higher would-be front curve and higher the plus power lower would be the front curve, but under both conditions’ vertex distance should be kept minimum. But as per Tshering’s ellipse the base curve values will not satisfy the superimposition condition of ghost images especially for lower powers and thus will never be in a sharp focus.

Ghost image 3 is formed due to reflections from cornea and front surface of lens and only come in sharp focus with high plus powered lens. Unlike ghost image 2 it depends not only upon front curve and the vertex distance of the lens but also on the thickness of the lens.

Ghost image 4 and 5 are almost similar in nature and are caused due to the light coming from behind of the lens i.e., from right to left direction. Reflection is seen as image of the wearers face on the back of the lens which is observed by wearer only. Although these two images are formed with much larger intensities as compared to other three still, they are least troublesome as a majority of light coming from behind is blocked by head and also a much larger size of lens is required to gain all the light coming from behind, and such a large size eyeglass are rarely seen, reflections are mostly seen when wearer’s face is highly illuminated. For distant objects reflections are only seen for high plus powers for certain values of base curve and back curve which could be eliminated through right form of lens hence they are not very much troublesome but if face is taken up as an object and that too with high illumination than the reflections are easily noticed for high minus power lenses and again the remedy is to alter the form of lens. Tinted lens like sunglasses are more prone to creating such type of ghost images as due to the tint the transmission is reduced and light energy is converted into reflection hence more prominent ghost images are formed and this also lead to causing disability glare especially on a bright sunny day near beaches or mountains. Its been found while uncoated clear and tint lenses that amount of reflection with a uncoated clear lens is about 4% whereas with tinted lens its around 20%. Hence majority of sunglasses are provided with a back side AR coat so as to eliminate the reflection as well as disability glare.

A particular type of ghost image is being formed in bifocals especially straight-line bifocals or E style bifocals due to the thick ridge dividing the distance and near portion. AR coat is applied on the lens and the ridge also occupies that coating which helps in reducing ghost images. Reflections are seen as vertical bars.

Another type of reflection named as veiling glare is the virtual image of the illuminated objects in the surrounding being formed due to reflection from both front and back surface of lens. Such type of reflection is somewhat like what is being formed by a curved mirror in which the reflected rays are made to intersect and form a virtual image. Wearers are not troubled with these reflections but the observe would always see a sort of image of himself or the surrounding on the lens of the wearer which makes eye contact quite disturbing. Along with veiling glare power rings are also experienced by the observer due to multiple internal reflection taking place at the edge of a minus power lens and as the thickness increases with power the reflection increases and creates more poor cosmetic appearance. Earlier the bevels were made darkened with some markers or with a very precise tinting at the edge only to reduce the effect of multiple reflections.

How Does Anti-Reflective Coatings Work

Reflected rays from front and back surface travel in a wave like pattern with troughs and crests of both the waves coinciding with each other making the two waves within same phase which leads to addition of reflected light energy hence reflection is observed this phenomenon is known as constructive interference. Anti-Reflective coatings works by making the two waves being out of phase exactly by half a wavelength due to which trough of one wave now coincides with crest of another wave, hence cancelling out the resultant wave thus eliminating reflection this phenomenon is known as destructive interference. To effectively cancel out the waves two conditions which are the path condition and the amplitude conditions must be satisfied.

Path condition-: This condition tells the thickness of the coating should be 1/4th of the wavelength of the light source used then only the reflected rays would be out of phase. Waves reaching the surface of the lens has to travel twice through the thin Anti-Reflective film which makes the waves to be exactly half a wavelength out of phase as compared to the waves reflecting from film’s surface.

Optimal thickness of Anti-Reflective Coating for a particular wavelength is calculated by (T=Wavelength/4*Refractive index of thin film). Elimination of reflected waves under this condition is valid for only light of particular wavelength and generally chosen wavelength is 555nm (yellow green) having the maximum luminous efficiency.

Amplitude Condition-: To exactly cancel out the two reflected waves from front and back surface the amplitudes and reflectance factor of both the waves should be equal and to satisfy this condition refractive index of the thin film should be equal to the square root of the refractive index of the lens used.

Reflectance factor of Air/Film interface(R1) =(Nf-Na/Nf+Na)

Reflectance factor of Film/Glass interface(R2) =(Ng-Nf/Ng+Nf) Keeping R1=R2

(Nf-Na/Nf+Na) sq=) = (Ng-Nf/Ng+Nf) sq =Nf=Sq root of Ng

Considering a glass lens with Refractive index 1.523 an ideal AR coating should have a refractive index of about 1.23 but no metal oxide has such a low refractive index and the nearest possible index is of around 1.38 which is of magnesium fluoride, hence magnesium fluoride is majorly used to coat a glass lens. But for magnesium fluoride both the amplitude and path condition together are not satisfied.

Comparing reflectance between an uncoated and coated glass lens with Refractive index of glass 1.523 and refractive index of coating used is 1.38(magnesium fluoride)

A1(Glass/Air interface) = (1.523-1/1.523+1) =0.2072

A2(Reflection Inside glass) = (1.523-1.523/1.523+1.523) =0

Reflectance=(A1-A2) sq=0.04289 i.e., 4.28% reflection

Now a thin magnesium oxide film of RI 1.38 has been added

A1(Film/Air interface) = (1.38-1/1.38+1) =0.15966

A2(Glass/Film interface) = (1.523-1.38/1.523+1.38) =0.05025

Reflectance=(A1-A2) sq=0.011970 i.e., 1.19% reflection

It could be clearly seen from above calculations there is more than 50% of reduction in reflection.

Multi – Layer Coatings

As we know that the path and amplitude condition together are not easily fulfilled along with that as per path condition the ideal thickness of the coating works only for a particular wavelength of light hence not much reduction is observed in the reflection and as per amplitude condition of a specific value of refractive index of thin film is suitable in eliminating the reflection but materials with such a low refractive indices are very brittle and robust hence can’t maintain adhesion on the lens surface for larger period of time and hence peels off easily.

To overcome these problems the concept of multi-layer anti reflection coating was introduced that incorporates multiple layers of metal oxides made with various thickness and refractive indices so as to eliminate as much reflection as possible. In such a system the amplitude of the waves reflected from the Air/1stFilm interface should be cancelled by the sum of amplitude of waves being reflected from interfaces between multiple layers. Due to these multiple layers of various thickness and refractive indices reflection is reduced for a wide spectrum of light. While comparing a single layer and multi-layer AR coating it was seen that for single layer coating the maximum reduction in reflection was more than the multi-layer coating but only for a single wavelength, whereas multi-layer coating reduces reflection with less amount compared to single layer but the reduction is for a wider range of spectrum, hence used widely. Adhesion of AR layers is not very good in case of plastic lenses like CR-39, hence multi-layer coating is placed in such a manner that the layer which is directly in contact with the lens surface is of a higher refractive index than of the lens which provides great adhesion and then alternate layer of low and high refractive indices material are used with the top most layer of titanium dioxide or zirconium dioxide.

These two-material act both as an anti-static as well as super-hydrophobic coating making lens easy to clean as well as retains less smudges. It is believed that these metal oxides react to some extent with atmospheric carbon or other sources of carbon to form C H bonds on the metal oxide surface. The existence of these C H bonds tends to reduce the Surface energy of that Surface and thus facilitate easy cleaning of the coated lens. Considering multi-layer coating, reflection of different wavelengths are reduced but with variable extent hence the colour depends on the wavelengths having maximum residual reflection.

Brands like Essilor have developed a coating having equal reduction of reflection for every wavelength of light, hence the colourless coating is observed also called achromatic coating. Like front surface same set of coatings are applied on the back surface of lens to reduce backside reflections.

Although multi-layered coating proves to be a good solution in reducing reflections and making the lens surface much transparent still it comes with few disadvantage with primary one being is that it scratches easily as compared to an uncoated lens and due to the thickness of the layers applied the optical properties of the lens are compromised a bit hence while manufacturing the lens a sharp sight has to be given over the thickness of the layers applied. The outer layer is to be kept within the range of 5-10 nm. The overall thickness of the anti-reflective stack has to be compensated for the additional outer layer of Titanium oxide or Zirconium oxide. Studies have shown that placing a 3nm layer of Titanium Oxide or 5nm layer of Zirconium Oxide give best results without compromising the optics of lens much.

Manufacturing of Anti-Reflective Lenses

The mechanism used for AR coating is called PVD (Physical Vapour Deposition) in which the solid metal oxide crystals are burnt under high temperature thus evaporate and settle on the lens surface. Along with PVD, Vacuum sputtering is primarily used for deposition of thin film of metal oxides on the lens surface. A chamber is constructed from which all of the air is evacuated and vacuum is created so as to prevent any atmospheric oxidation and to eliminate any impurities present.

After that argon air which is least reactive gas is passed into the chamber which is made to be ionized by passing electric current in the chamber. At the negative side the metal oxides are placed in different compartments When the current is passed the argon gas atoms gets excited and they rush towards the negatively charges metal oxides and due to this strike with a heavy force, atoms from metal oxides are released or bombarded and start moving toward the positively charged plate over which lens to be coated is placed. A shutter is placed over compartments of metal oxide so that the amount of their deposition could be controlled as per required thickness. A dome shaped plate having multiple holes in it where lenses are placed is fitted towards the positive end.

The distance of each lens from the coating material is same hence equal amount of layer is deposited on each lens. Prior to AR coat lenses are slowly passed through a liquid bath of a solvent based hard coat where the coating solution adheres to both convex and concave sides of the lens. The hard coat is then allowed to cure in a high temperature oven until stable.

Before placing the lenses in vacuum chamber, they are thoroughly cleaned both manually and under UV light so as to eliminate any sort of impurities on the surface of lens. The room in which AR coating is done is fully air conditioned and made totally dust free to ensure that airborne dust do not settle on the lens surface while placing them in the chamber. After the front surface of the lens gets coated then the metal plate is reversed and back surface is placed for coating. It takes almost 1.5 hours per side to get coated and depending upon the size of the vacuum chamber multiple dome shaped metal plates could be placed and around 100 lenses could be coated together. Most commonly used materials for an AR coat are Titanium Dioxide, Silicone Dioxide, Zirconium Dioxide and Magnesium Fluoride.

References:-

1) Principle of Ophthalmic Lenses by M.O. Jal

2) United States US 20080028984A1 (12) Patent Application Publication (10) Pub. No.: US 2008/0028984 A1 Meredith et al. (43) Pub. Date: Feb. 7, 2008 (54) ANTI-REFLECTIVE COATING FOR A (86). PCT No.: PCT/USO4/34527 SUBSTRATE S 371(c)(1), 2), (4) Date: Apr. 12, 2007 (75) Inventors: William A. Meredith, Faribault, MN (2), (4) p 9 O O (US); Joel T. Anderson, Cottage Grove, Related U.S. Application Data MN (US); John R. German, Prairie Du (60) Provisional application No. 60/514,936, filed on Oct. Sac, WI (US); Daniel P. Woodruff, 28, 2003. Lakeville, MN

 

 

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