Dynamic range
Encyclopedia
Dynamic range, abbreviated DR or DNR, is the ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...

between the largest and smallest possible values of a changeable quantity, such as in sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

and light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

. It is measured as a ratio, or as a base-10
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

(decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

) or base-2
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

(doubling
Doubling
Doubling may refer to:*in math:**multiplication by 2**doubling the cube, a geometric problem**doubling time, the period of time required for a quantity to double in size or value**doubling map**period-doubling bifurcation***in music:...

s, bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

s or stops) logarithmic
Logarithmic scale
A logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself.A simple example is a chart whose vertical axis increments are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4...

value.

## Dynamic range and human perception

 Factor (power) Decibels Stops 1 0 0 2 3.01 1 3.16 5 1.66 4 6.02 2 5 6.99 2.32 8 9.03 3 10 10 3.32 16 12.0 4 20 13.0 4.32 31.6 15 4.98 32 15.1 5 50 17.0 5.64 100 20 6.64 1 000 30 9.97 1 024 30.1 10 10 000 40 13.3 100 000 50 16.6 1 000 000 60 19.9 1 048 576 60.2 20 100 000 000 80 26.6 1 073 741 824 90.3 30 10 000 000 000 100 33.2

The human senses of sight
Visual perception
Visual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...

and hearing have a very high dynamic range. A human is capable of hearing (and usefully discerning) anything from a quiet murmur in a soundproofed room to the sound of the loudest heavy metal concert. Such a difference can exceed 100 dB
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

which represents a factor of 100,000 in amplitude and a factor 10,000,000,000 in power. A human can see objects in starlight (although colour differentiation
Color vision
Color vision is the capacity of an organism or machine to distinguish objects based on the wavelengths of the light they reflect, emit, or transmit...

is reduced at low light levels) or in bright sunlight, even though on a moonless night objects receive 1/1,000,000,000 of the illumination they would on a bright sunny day: that is a dynamic range of 90 dB. A human cannot perform these feats of perception at both extremes of the scale at the same time. The eyes take time to adjust to different light levels and the dynamic range of the human eye in a given scene is actually quite limited due to optical glare
Glare
Glare may refer to:* Glare is difficulty seeing in the presence of very bright light* A glare is a facial expression of squinted eyes and look of contempt* A call collision in telecommunications* GLARE, an advanced aerospace material...

. The instantaneous dynamic range of human audio perception is similarly subject to masking
Auditory masking occurs when the perception of one sound is affected by the presence of another sound.- Simultaneous masking :Simultaneous masking is when a sound is made inaudible by a "masker", a noise or unwanted sound of the same duration as the original sound.-Critical bandwidth:If two sounds...

, so that, for example, a whisper cannot be heard in loud surroundings. Nevertheless, a good quality audio reproduction system should be able to reproduce accurately both the quiet sounds and the loud; similarly, a good quality visual display system should be able to capture both shadow details in nighttime scenes and bright areas of sunny scenes.

In practice, it is difficult to achieve the full dynamic range experienced by humans using electronic equipment. Electronically reproduced audio and video often uses some trickery to fit original material with a wide dynamic range into a narrower recorded dynamic range that can more easily be stored and reproduced: these techniques are called dynamic range compression. For example, a good quality LCD display has a dynamic range of around 1000:1 (commercially the dynamic range is often called the "contrast ratio
Contrast ratio
The contrast ratio is a property of a display system, defined as the ratio of the luminance of the brightest color to that of the darkest color that the system is capable of producing...

" meaning the full-on/full-off luminance
Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...

ratio), and some of the latest CMOS
CMOS
Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...

image sensors now have measured dynamic ranges of about 11,000:1 (reported as 13.5 stops, or doubling
Doubling
Doubling may refer to:*in math:**multiplication by 2**doubling the cube, a geometric problem**doubling time, the period of time required for a quantity to double in size or value**doubling map**period-doubling bifurcation***in music:...

s, equivalent to binary
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

s). Paper reflectance can achieve a dynamic range of about 100:1. Professional ENG Camcorders such as Sony Digital Betacam currently achieves dynamic ranges of greater than 90dB in audio recording.

When showing a movie or a game, a display is able to show both shadowy nighttime scenes and bright outdoor sunlit scenes, but in fact the level of light coming from the display is much the same for both types of scene (perhaps different by a factor of 10). Knowing that the display does not have a huge dynamic range, the program makers do not attempt to make the nighttime scenes millions of times less bright than the daytime scenes, but instead use other cues to suggest night or day. A nighttime scene will usually contain duller colours and will often be lit with blue lighting, which reflects the way that the human eye sees colours at low light levels.

### Audio

Audio engineers often use dynamic range to describe the ratio of the amplitude of the loudest possible undistorted sine wave
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

to the root mean square
Root mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...

(rms) noise amplitude, say of a microphone
Microphone
A microphone is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1877, Emile Berliner invented the first microphone used as a telephone voice transmitter...

or loudspeaker
Loudspeaker
A loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...

.

The dynamic range of human hearing is roughly 140 dB. The dynamic range of music as normally perceived in a concert hall doesn't exceed 80 dB, and human speech is normally perceived over a range of about 40 dB.

The dynamic range differs from the ratio of the maximum to minimum amplitude a given device can record, as a properly dither
Dither
Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images...

ed recording device can record signals well below the rms noise amplitude (noise floor).

For example, if the ceiling of a device is 5V (rms) and the noise floor is 10uV (rms) then the dynamic range is 500000:1, or 114 dB:

In digital audio theory the dynamic range is limited by quantization error
Quantization error
In analog-to-digital conversion, the difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding or truncation...

. The maximum achievable dynamic range for a digital audio system with Q-bit uniform quantization is calculated as the ratio of the largest sine-wave rms to rms noise is:

The maximum achievable signal-to-noise ratio
Signal-to-noise ratio
Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...

(SNR) for a digital audio system with Q-bit uniform quantization is

The 16-bit compact disc
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

has a theoretical dynamic range of about 96 dB (or about 98 dB for sinusoidal signals, per the formula). Digital audio with 20-bit digitization is theoretically capable of 120 dB dynamic range; similarly, 24-bit digital audio calculates to 144 dB dynamic range. All digital audio recording and playback chains include input and output converters and associated analog circuitry, significantly limiting practical dynamic range. Observed 16-bit digital audio dynamic range is about 90 dB.

Dynamic range in analog audio is the difference between low-level thermal noise in the electronic circuitry and high-level signal saturation resulting in increased distortion and, if pushed higher, clipping
Clipping (audio)
Clipping is a form of waveform distortion that occurs when an amplifier is overdriven and attempts to deliver an output voltage or current beyond its maximum capability...

. Multiple noise processes determine the noise floor of a system. Noise can be picked up from microphone self-noise, preamp noise, wiring and interconnection noise, media noise, etc. Early 78 rpm phonograph discs had a dynamic range of up to 40 dB, soon reduced to 30 dB and worse due to wear from repeated play. German magnetic tape in 1941 was reported to have had a dynamic range of 60 dB, though modern day restoration experts of such tapes note 45-50 dB as the observed dynamic range. Ampex
Ampex
Ampex is an American electronics company founded in 1944 by Alexander M. Poniatoff. The name AMPEX is an acronym, created by its founder, which stands for Alexander M. Poniatoff Excellence...

tape recorders in the 1950s achieved 60 dB in practical usage, though tape formulations such as Scotch 111 boasted 68 dB dynamic range. In the 1960s, improvements in tape formulation processes resulted in 7 dB greater range, and Ray Dolby developed the Dolby A-Type noise reduction system that increased low- and mid-frequency dynamic range on magnetic tape by 10 dB, and high-frequency by 15 dB, using companding
Companding
In telecommunication, signal processing, and thermodynamics, companding is a method of mitigating the detrimental effects of a channel with limited dynamic range...

(compression and expansion) of four frequency bands. The peak of professional analog magnetic recording tape technology reached 90 dB dynamic range in the midband frequencies at 3% distortion, or about 80 dB in practical broadband applications. The Dolby SR noise reduction system gave a 20 dB further increased range resulting in 110 dB in the midband frequencies at 3% distortion. Compact Cassette
Compact Cassette
The Compact Cassette, often referred to as audio cassette, cassette tape, cassette, or simply tape, is a magnetic tape sound recording format. It was designed originally for dictation, but improvements in fidelity led the Compact Cassette to supplant the Stereo 8-track cartridge and reel-to-reel...

tape performance ranges from 50 to 56 dB depending on tape formulation, with Metal Type IV tapes giving the greatest dynamic range, and systems such as XDR
XDR (audio)
XDR is a quality-control and duplication process for the mass-production of pre-recorded audio cassettes. It is a process designed to provide higher quality audio on pre-recorded cassettes by checking the sound quality at all stages of the tape duplication process...

, dbx
Dbx (noise reduction)
dbx is a family of noise reduction systems developed by the company of the same name. The most common implementations are dbx Type I and dbx Type II for analog tape recording and, less commonly, vinyl LPs. A separate implementation, known as dbx-TV, is part of the MTS system used to provide stereo...

and Dolby noise reduction system
Dolby noise reduction system
Dolby NR is the name given to a series of noise reduction systems developed by Dolby Laboratories for use in analog magnetic tape recording. The first was Dolby A, a professional broadband noise reduction for recording studios in 1966, but the best-known is Dolby B , a sliding band system for the...

increasing it further. Specialized bias and record head improvements by Nakamichi and Tandberg combined with Dolby C noise reduction yielded 72 dB dynamic range for the cassette. Vinyl microgroove phonograph records typically yield 55-65 dB, though the first play of the higher-fidelity outer rings can achieve a dynamic range of 70 dB. The rugged elements of moving-coil microphones can have a dynamic range of up to 140 dB (at increased distortion), while condenser microphones are limited by the overloading of their associated electronic circuitry. Practical considerations of acceptable distortion levels in microphones combined with typical practices in a recording studio result in a useful operating range of 125 dB.

In 1981, researchers at Ampex determined that a dynamic range of 118 dB on a dithered digital audio stream was necessary for subjective noise-free playback of music in quiet listening environments.

Since the early 1990s, it has been recommended by several authorities, including the Audio Engineering Society
Audio Engineering Society
Established in 1948, the Audio Engineering Society draws its membership from amongst engineers, scientists, other individuals with an interest or involvement in the professional audio industry. The membership largely comprises engineers developing devices or products for audio, and persons working...

, that measurements of dynamic range be made with an audio signal present, which is then filtered out to get the noise floor. This avoids questionable measurements based on the use of blank media, or muting circuits.

### Electronics

Electronics
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

engineers apply the term to:
• the ratio of a specified maximum level of a parameter
Parameter
Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....

, such as power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

, current, voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

or frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

, to the minimum detectable value of that parameter. (See Audio system measurements
Audio system measurements
Audio system measurements are made for several purposes. Designers take measurements so that they can specify the performance of a piece of equipment. Maintenance engineers make them to ensure equipment is still working to specification, or to ensure that the cumulative defects of an audio path are...

.)
• In a transmission system
Transmission system
In telecommunications a transmission system is a system that transmits a signal from one place to another. The signal can be an electrical, optical or radio signal....

, the ratio of the overload

level (the maximum signal power that the system can tolerate without distortion
Distortion
A distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice...

of the signal) to the noise level of the system.
• In digital
Digital
A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...

systems or devices, the ratio of maximum and minimum signal levels required to maintain a specified bit error ratio
Bit error ratio
In digital transmission, the number of bit errors is the number of received bits of a data stream over a communication channel that have been altered due to noise, interference, distortion or bit synchronization errors....

.

In audio and electronics applications, the ratio involved is often so huge that it is converted to a logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

and specified in decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

s.

### Metrology

In metrology
Metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

, such as when performed in support of science, engineering or manufacturing objectives, dynamic range refers to the range of values that can be measured by a sensor or metrology instrument. Often this dynamic range of measurement is limited at one end of the range by saturation of a sensing signal sensor or by physical limits that exist on the motion or other response capability of a mechanical indicator. The other end of the dynamic range of measurement is often limited by one or more sources of random noise
Noise
In common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical noise...

or uncertainty in signal levels that may be described as the defining the sensitivity
Sensitivity (electronics)
The sensitivity of an electronic device, such as a communications system receiver, or detection device, such as a PIN diode, is the minimum magnitude of input signal required to produce a specified output signal having a specified signal-to-noise ratio, or other specified criteria.Sensitivity is...

of the sensor or metrology device. When digital sensors or sensor signal converters are a component of the sensor or metrology device, the dynamic range of measurement will be also related to the number of binary digits (bits) used in a digital numeric representation in which the measured value is linearly related to the digital number. For example, a 12-bit digital sensor or converter can provide a dynamic range in which the ratio of the maximum measured value to the minimum measured value is up to 212 = 4096. With gamma correction
Gamma correction
Gamma correction, gamma nonlinearity, gamma encoding, or often simply gamma, is the name of a nonlinear operation used to code and decode luminance or tristimulus values in video or still image systems...

, this limitation can be relaxed somewhat; for example, the 8-bit encoding used in sRGB image encoding represents a maximum to minimum ratio of about 3000.

Metrology systems and devices may use several basic methods to increase their basic dynamic range. These methods include averaging and other forms of filtering, repetition of measurements, nonlinear transformations to avoid saturation, etc. In more advance forms of metrology, such as multiwavelength digital holography
Digital holography
Digital holography is the technology of acquiring and processing holographic measurement data, typically via a CCD camera or a similar device. In particular, this includes the numerical reconstruction of object data from the recorded measurement data, in distinction to an optical reconstruction...

, interferometry
Interferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...

measurements made at different scales (different wavelengths) can be combined to retain the same low-end resolution while extending the upper end of the dynamic range of measurement by orders of magnitude.

### Music

In music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

, dynamic range is the difference between the quietest and loudest volume of an instrument
Musical instrument
A musical instrument is a device created or adapted for the purpose of making musical sounds. In principle, any object that produces sound can serve as a musical instrument—it is through purpose that the object becomes a musical instrument. The history of musical instruments dates back to the...

, part
Part
Part may refer to:*Part *Part , a relation in mereology*Part , the music played or sung by an individual instrument or voice*Parts , a 1997 children's book by Tedd Arnold...

or piece of music. In modern recording, this range is often limited through audio level compression
Audio level compression
Dynamic range compression, also called DRC or simply compression reduces the volume of loud sounds or amplifies quiet sounds by narrowing or "compressing" an audio signal's dynamic range...

, which allows for louder volume, but can make the recording sound less exciting or live. Popular music
Popular music
Popular music belongs to any of a number of musical genres "having wide appeal" and is typically distributed to large audiences through the music industry. It stands in contrast to both art music and traditional music, which are typically disseminated academically or orally to smaller, local...

typically has a dynamic range of 6 to 10 dB, with some forms of music having as little as 1 dB or as much as 15 dB. See Loudness war
Loudness war
The loudness war or loudness race is a pejorative term for the apparent competition to digitally master and release recordings with increasing loudness.The phenomenon was first reported with respect to mastering practices for 7" singles...

### Photography

Photographer
Photography
Photography is the art, science and practice of creating durable images by recording light or other electromagnetic radiation, either electronically by means of an image sensor or chemically by means of a light-sensitive material such as photographic film...

s use "dynamic range" for the luminance
Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...

range of a scene being photographed, or the limits of luminance range that a given digital camera
Digital camera
A digital camera is a camera that takes video or still photographs, or both, digitally by recording images via an electronic image sensor. It is the main device used in the field of digital photography...

or film
Photographic film
Photographic film is a sheet of plastic coated with an emulsion containing light-sensitive silver halide salts with variable crystal sizes that determine the sensitivity, contrast and resolution of the film...

can capture,
or the opacity range of developed film images, or the reflectance range of images on photographic papers.

A graduated neutral density filter, also known as a graduated ND filter, split neutral density filter, or just a graduated filter, is an optical filter that has a variable light transmission. Typically half of the filter is of neutral density which transitions, either abruptly or gradually, into...

s are used to decrease the dynamic range of scene luminance that can be captured on photographic film
Photographic film
Photographic film is a sheet of plastic coated with an emulsion containing light-sensitive silver halide salts with variable crystal sizes that determine the sensitivity, contrast and resolution of the film...

(or on the image sensor
Image sensor
An image sensor is a device that converts an optical image into an electronic signal. It is used mostly in digital cameras and other imaging devices...

of a digital camera
Digital camera
A digital camera is a camera that takes video or still photographs, or both, digitally by recording images via an electronic image sensor. It is the main device used in the field of digital photography...

): The filter is positioned in front of the lens at the time the exposure is made; the top half is dark and the bottom half is clear. The dark area is placed over a scene's high-intensity region, such as the sky. The result is more even exposure in the focal plane, with increased detail in the shadows and low-light areas. Though this doesn't increase the fixed dynamic range available at the film or sensor, it stretches usable dynamic range in practice.

The dynamic range of sensors used in digital photography is many times less than that of the human eye and generally not as wide as that of chemical photographic media. In the domain of digital imaging, algorithms have been developed to map the image differently in shadow and in highlight in order to better distribute the lighting range across the image. These techniques are known as local tone mapping, and usually involves overcoming the limited dynamic range of the sensor array by selectively combining multiple exposures of the same scene in order to retain detail in light and dark areas. The same approach has been used in chemical photography to capture an extremely wide dynamic range: A three-layer film with each underlying layer at 1/100 the sensitivity of the next higher one has, for example, been used to record nuclear-weapons tests.

The most severe dynamic-range limitation in photography may not involve encoding, but rather reproduction to, say, a paper print or computer screen. In that case, not only local tone mapping, but also dynamic range adjustment can be effective in revealing detail throughout light and dark areas: The principle is the same as that of dodging and burning (using different lengths of exposures in different areas when making a photographic print) in the chemical darkroom. The principle is also similar to gain riding or automatic level control in audio work, which serves to keep a signal audible in a noisy listening environment and to avoid peak levels which overload the reproducing equipment, or which are unnaturally or uncomfortably loud.

• Loudness war
Loudness war
The loudness war or loudness race is a pejorative term for the apparent competition to digitally master and release recordings with increasing loudness.The phenomenon was first reported with respect to mastering practices for 7" singles...

• High dynamic range imaging
High dynamic range imaging
In image processing, computer graphics, and photography, high dynamic range imaging is a set of techniques that allows a greater dynamic range between the lightest and darkest areas of an image than current standard digital imaging techniques or photographic methods...