In this explainer, we will learn how to describe how the phase differences of coherent light waves can be used to produce three-dimensional images.
The word “hologram” is loosely used outside of physics to refer to any kind of three-dimensional projected image. In physics, a hologram is defined more specifically as an image generated by interference between coherent light waves. Holograms in physics are in fact three-dimensional projected images, so the generic understanding of what holograms are is consistent with the meaning in physics, if not how such images are produced and viewed.
A holographic image can be compared to a photographic image. There are two basic ways in which photographic and holographic images can be compared: how they are produced and how they are viewed.
For simplicity, we will not consider color images in the discussion, only monochromatic images.
An analog monochromatic photographic image is produced by using a photographic plate. A photographic plate is a flat surface that chemically changes when exposed to visible light.
Visible light from an object is required. The light from the object does not need to be coherent. Light from the object passes through a lens that focuses light rays from the object to form a real image of the object on the plate. Light from a given point on the object corresponds to a given point on the image, which is recorded on the plate. The plate is now known as a photograph.
When the image is recorded, the photograph is chemically treated so that it no longer reacts to light. Afterward, the photograph is viewed simply by reflecting light from the photograph. Again, this light does not need to be coherent.
A photograph records the intensity of light at each point in an image. Nothing about such an intensity has any exact relationship with the distance from a point on the object imaged to the corresponding point on the image.
The lack of any clear relationship between the intensity of light at a point on an image and the distance from the corresponding point on the object means that photographs are two-dimensional images.
Consider the photograph shown in the following figure.
It is not possible to tell from the photograph which of the two objects shown is larger. The triangle fills more of the photograph than the circle does, but this may be because it is closer than the circle rather than larger than it.
For objects at significantly different distances from a lens, the lens can only produce a sharp image of one of the objects. This is represented in the following figure.
A more realistic version of the photograph would look more like the following figure if the two objects were at significantly different distances.
From this photograph, we could see that the two objects were not at the same distance away from the lens that produced the image, but we would not be able to tell which object is closer and which is further away. Also, it is possible that the triangle had an irregular surface and only appeared to be blurred because of this texture, in which case the two objects might actually have been at similar distances from the lens.
A holographic image is different to this. In a holographic image, the distances traveled by light from different points on objects are recorded in the image. Light from different points on an object travels different distances to a viewer depending on the direction that the light travels to reach the viewer, so this means that a holographic image of an object allows the image of the object to be viewed from different directions.
Let’s now see how a holographic image is recorded.
The following figure shows the apparatus setup used to record a holographic image of a cylinder.
We can see that this setup differs to that used for recording a photographic image in several ways, such as the following:
- A coherent light source is required. This is usually a laser.
- No convex lens is used.
- No real image is formed.
- Some of the light used to form the holographic image does not come into contact with the object.
Let’s first consider that the holographic plate receives light both from the object and directly from the light source. The light from the object is called the object beam and the light from the source is called the reference beam. These are shown in the following figure.
The light incident on the holographic plate is described as consisting of beams rather than of rays. The beams consist of diverging rays. The difference traveled by waves that follow different ray paths is called the difference of the path lengths of the waves.
It is useful to note that the beam that passes from the light source to the object is called an illumination beam. The entire beam from the source to the holographic plate is called the reference beam, however.
Let’s now look at an example in which the path lengths of waves used in recording a holographic image are considered.
Example 1: Comparing the Path Lengths of Beams Used in Recording a Holographic Image
The diagram shows some apparatus used in holography, including a cylindrical object.
- Which of the following is true of the path lengths of
the beam paths ABC and ABD?
- The path lengths are the same.
- ABC is longer than ABD.
- ABD is longer than ABC.
- Which of the following is true of the path lengths
of the beam paths AbcC and AbdD?
- AbdD is longer than AbcC.
- AbcC is longer than AbdD.
- The path lengths are the same.
The paths ABC and ABD are followed by rays at opposite edges of the reference beam. The paths are identical until they reach the center of a diverging lens. After the diverging lens, the ray that reaches C and the ray that reaches D are deflected by equal angles, as the rays are equal distances from the center of the lens when they reach the lens. This shows us that the lengths of the paths ABC and ABD are the same.
The paths AbcC and AbdD are followed by rays at opposite edges of the object beam. The paths are also identical until they reach the center of a diverging lens. After the diverging lens, however, the ray that travels to d travels further than the ray that travels to c. The ray that travels to D from d then travels further between these points than the ray that travels to C from c does. We see then that AbdD is longer than AbcC.
The light source used to produce the rays in both beams is coherent. This means that any two light waves that travel the same path length and undergo equal numbers of reflections have the same phase as each other when they reach the holographic plate.
Light waves from both beams are reflected twice between emission from the light source and absorption by the holographic plate, so only the path length difference actually affects the phase difference between two such waves when they reach the holographic plate.
Let’s now look at an example in which the phase differences of waves used in recording a holographic image are considered.
Example 2: Comparing the Phases of Light Waves used in Recording a Holographic Image
The diagram shows some apparatus used in holography, including a cylindrical object.
- Which of the following is true of the phase difference
between light waves that travel the path ABC and those that travel
the path ABD?
- The phase difference is zero.
- There is a nonzero phase difference between the waves.
- Which of the following is true of the phase difference
between light waves that travel the path AbcC and those that
travel the path AbdD?
The path lengths of ABC and ABD are equal. The light that travels the paths is coherent, and so the light waves at the ends of these paths have the same phase as each other. The phase difference of the waves is zero.
The path lengths of AbcC and AbdD are unequal. This does not necessarily mean that there is a phase difference between the waves that travel these paths. It is possible that the path difference is equal to an integer number of wavelengths of the light that travels these paths. If the path difference is equal to , where is an integer and is the wavelength of the light, the waves will have zero phase difference. It is then possible for the phase difference of the waves to have any value between 0 and . Denoting the phase difference as , we have
For each point on the holographic plate, light waves arrive at the point from the object beam and from the reference beam. The holographic plate records the phase difference between the waves from these two beams. The phase difference at a point will depend on the distance of the point on the holographic plate from a point on the object.
Each point on a holographic plate, as well as recording the intensity of light reflected from the object that reached the point, records the phase difference of the object beam and reference beam at that point. The material of the holographic plate is altered by the light that it absorbs, similarly to the case of a photographic plate. The appearance of the holographic plate is therefore changed when it records an image.
The phase differences between the object and reference beams recorded at points on a holographic plate correspond to the differences in distance from the imaged object and the holographic plate at those points.
It is important to understand that a holographic image of a realistic object rather than a simple perfect geometric shape is greatly affected by the irregularity of the surface of such an object. The diagrams used in the explainer show reflection from smooth surfaces, specular reflection. Reflection from the surface of a realistic object is diffuse. This is represented in the following figure.
This means that two points very close together on an object could reflect rays at very different angles. A more realistic representation of an object beam would be closer to the following figure.
We can see that rays from points very close to either the top or the bottom of the imaged object can be reflected to points covering the whole of the holographic plate. The same applies to any other point on the object, not just the top and the bottom. The effect of this is that each point on a holographic plate receives some light from almost every point on the imaged object.
It is important to recognize that, unlike in the case of the formation of a photographic image, no converging lens is placed between the object and the holographic plate, so diffuse rays are not focused.
Both phase differences and diffuse reflection effects mean that a holographic plate does not record an image of an object that can be viewed just using ordinary reflected light. If a holographic plate is viewed by reflecting ordinary light from it, as is the case with a photograph, all that will be seen will be a confusing pattern of dark and light patches.
Let’s now look at an example in which the appearance of a holographic plate is considered.
Example 3: Describing the Appearance of a Holographic Plate Using Incoherent White Light
Which of the figures most closely resembles the appearance of a part of a holographic plate that has recorded an image of a cat? The figures are not necessarily of equal area parts of the holographic plate. The figures represent the appearance of sections of the holographic plate, not the appearance of the image that would be formed by such a section of the plate by transmitting a laser beam through the plate.
The light that is incident on a holographic plate does not form a real image of the object. If the object imaged is a cat, the holographic plate will not have on it a real image of a cat.
If a holographic plate will not have on it a real image of a cat, neither will it contain multiple real images of a cat. Any of the options showing real images of a cat are incorrect.
The only option in which no real image of a cat is present is the following.
This represents a close-up view of the surface of a holographic plate. The plate shows only a pattern of light and dark patches when viewed using incoherent white light.
To view a holographic image that has been recorded in such a way that the image is recognizable, it is necessary to use coherent light. The coherent light used must be of the same wavelength as the light used to record the holographic image.
A beam of coherent light of the correct wavelength can be made incident on a holographic plate that has recorded an image. This beam consists of parallel rays. The beam is incident on the holographic plate at the same angle as the reference beam that was used when the image was formed on the holographic plate. The term for the beam used to replay the holographic image is the playback beam.
When a holographic plate that has had an image recorded onto it then has a playback beam directed through it, the light at each point on the holographic plate is diffracted by the holographic plate. The diffracted light from different points on the holographic plate interferes. This is shown in the following figure.
The interfering light waves from the holographic plate produce a virtual image of an object imaged on the holographic plate. The image produced represents the distances between the points on the object that was imaged and so appears three-dimensional to a viewer.
A replayed holographic image has another interesting property, which is that if the playback beam is incident at some angle other than the angle at which the reference beam used to form the image on the holographic plate was incident, the resulting interference between the waves in the playback beam is changed. The changed interference pattern produces a changed image.
The change in a replayed image that results from a change in the angle of incidence of the playback beam is that the same object is imaged, but the angle from which the object is viewed is changed proportionally to the change in the playback beam angle. This is represented in the following figure.
Let’s now look at an example involving a replayed holographic image.
Example 4: Identifying the Holographic Image Seen by a Viewer
The diagram shows a laser being used to record a holographic image of a cylindrical object and then to display the image recorded on the holographic plate. Which of the virtual images would be observed by a viewer at the position shown?
- Virtual image B
- Virtual image A
- Both virtual images simultaneously
- Each virtual image would alternate.
- Neither virtual image
The eye of the viewer is shown to be at a position that is not along the line of the playback beam used to replay the recorded holographic image. This position difference of the viewer and the line of the playback beam has an equivalent effect to the changing of the direction of the playback beam. This means that the viewer would not see a virtual image that was identical to the recorded object. The viewer does not then see virtual image A.
If virtual image A will not be seen alone, then it will not be seen simultaneously or alternatingly with another virtual image, so the options stating that both virtual images would be seen can be eliminated.
Light passing through the holographic plate can reach the eye of the viewer, so it is not correct to say that no virtual image is seen.
The correct option is that virtual image B would be seen. Virtual image B is an image of the object that was recorded but viewed from a different position. The change in the position from which the object is viewed corresponds to the change in the position of the viewer’s eye.
An interesting property of holographic images results from the diffuse reflection of light from an imaged object. We recall that this results in light from points very close together on an object being incident at points more or less anywhere on a holographic plate. This means that each point on a holographic plate can have received light from almost the entire object that was imaged.
If a holographic plate is broken into fragments, each fragment will consist of many points that have each received light from almost the entire object that was imaged.
Let us now look at an example involving the replayed image produced by parts of a holographic plate.
Example 5: Identifying the Holograph Produced by a Fragment of a Holographic Plate
If a holographic plate was broken into pieces and a laser was used to view the image contained on one of the pieces, which of the following would the image show?
- The image that was contained on the whole of the plate but at a lower resolution
- A part of the object of a size proportional to the size of the piece of the plate
- A part of the object that had not been scanned by the object beam when the holographic image was formed
- An interference pattern
The question states that a laser is used to view the image on the pieces of the holographic plate, and so a virtual image of something would be seen rather than nothing or an interference pattern. These options can be eliminated.
Any part of an object that was not scanned by the object beam when the image was recorded cannot be part of the holographic image recorded, so the option that an unscanned part of the object would be seen cannot be correct.
For a photographic image, the obviously correct option would be that a part of the imaged object would be seen. This is not correct for a holographic image, however, as each point on a holographic plate can have received light from almost the entire object that was imaged. This means that any part of the holographic plate can reconstruct the image of the object that was imaged. A part of a holographic plate did not receive all the light from the object that was received by the whole of the holographic plate, however, so the image produced by a fragment of the plate would be an imperfect blurred version of the image that would be produced by the whole holographic plate. The resolution of the replayed image would be lower.
Let us now summarize what has been learned in this explainer.
- A holographic image is a three-dimensional virtual image of an object.
- Coherent light is required to record and to replay a holographic image.
- A holographic image records the phase differences between the light waves from different points on an object.
- The phase differences between the light waves from different points on an object depend on the path length differences of light waves from those points on the object to the holographic plate where the image of the object is recorded.
- Recording a holographic image requires a reference beam and an object beam.
- Replaying a holographic image requires a playback beam of the same wavelength of light used in the reference and object beams.
- A replayed holographic image can be viewed from positions other than the position that the imaged object was in relative to the holographic plate onto which it was imaged.
- Fragments of a holographic plate produce the same image as the entire holographic plate but at a lower resolution.