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UPDATED EXTRACT FROM CREG JOURNAL. FILE: FOOT3-UP.DOC REV. 8. LAST SAVED: 01/02/01 15:14 PHOTOMETRICS Foot-Candles: Photometric Units

More footnotes on optical topics. David Gibson describes the confusing range of photometric units.

A discussion of photometric units may the ratio of luminous efficiency to luminous The non-SI unit mean spherical candle- seem out of place in an electronic journal but efficiency at the wavelength where the eye is power is the intensity of a source if its engineers frequently have to use light sources most sensitive. Unfortunately, however, this output were spread evenly in all directions. It and detectors. The units of are term can be confused with the term efficacy, is therefore equivalent to the flux [lm] ¸ 4p. some of the most confusing and least which is used to describe the efficiency at standardised of units. converting electrical to luminous power. Photometric units are not difficult to The measures the intensity of a understand, but can be a minefield to the Illumination, Luminous Emittance. point source. We also need to define the uninitiated since many non-SI units are still The illumination of a surface is the properties of an extended source. Each small in use, and there are subtle differences incident power flux density measured in element DS of a diffuse reflective surface will between quantities with similar names, such lumens per square metre. A formal definition scatter the incident flux DF and behave as if as illumination and luminance. would be along the lines of: if a flux DF is it were an infinitesimal point source. The Here I will give explanations of the more incident over an area DS at an angle q to the ‘brightness’ of an extended surface is there- common units, but I will not digress into normal, then the flux density, E, is given by fore measured in per square metre. some of the more specialised applications. DF Luminance, as the property is called, can E = lim cosq (1) These include how photographic film speeds DS®0 DS refer to reflective surfaces or self-luminous are defined, and why the “f/ number” of a Emitted flux (or luminous emittance) surfaces such as a c.r.t., fluorescent tube, lens is important (when it is not important, can be defined in the same way. The lm/m2 is diffuse lamp housing, or the sky – see box. In when “ factor” is important too). given the name (abbreviation lx) when it general, luminance depends on direction. The This information is necessary for the design refers to illumination, but not when it refers fact that the direction can only be defined for of photometers and exposure meters, but is to luminous emittance, for which the unit a very small area can be a source of outside the scope of this article. lm/m2 is retained. confusion, given that the property itself refers to large areas. Definitions (“Candlepower”) Suppose an element of area DS shines

When considering the brightness of a with an intensity DIq at an angle q. The Radiant and . source we need to know the angular distribu- element of area projected at angle q is DS Light is a form of electromagnetic tion of the flux. This is called the luminous cosq so we can define the luminance in energy, and its power flux can be measured intensity and is measured in lumens per direction q as 1 DI in . This is the SI unit of power, and of for which we use the name L(q) = lim q (4) . Since many measurements of candela. If a flux DF is emitted in a solid DS®0 DS cosq light are connected with the response of the angle DW then the angular distribution of the There are a particular class of surfaces human eye, measuring power in this way flux can be given by called perfectly diffuse or surfaces does not give an indication of the ‘bright- DF for which the intensity varies with angle in I(q) = lim (2) ness’ of an object. A weighted power ®0 such a way that measurement is used, called the . This Note that the lumen and candela describe DI = DI cosq (5) is the SI unit of luminous flux. the properties of a point in space. Other units q n

The adjective ‘luminous’ refers to the are used to describe the properties of where In is the luminous intensity in the fact that the power is weighted according to extended surfaces. Luminous intensity should normal direction. For these surfaces it can be the response of the human eye. Two response always have the direction specified since it is seen that the luminance is constant with curves (for photopic and scotopic vision) are defined as the element of flux DF in a cone direction, being equal to DIn/DS. Such a usually used and have been defined and stan- of width DW in direction q. surface appears equally bright from all dardised by the C.I.E. (Commission Interna- The relationship between W directions. tionale de l’Eclairage). and cone full-angle q is given below. The continued on page 10 One way of defining the lumen (though approximation (q in degrees) is true to 2% not the SI method) would be to relate it to for q<60°; 5% for q<90°. The brightness of the sky these response curves, where 1W of radiant W = 2p(1- cos 1 q)» 0.00024 q2 (3) On a clear day, illumination from the sun is power at 555nm (peak sensitivity) corre- 2 about 50,000lx, but it can vary from 130,000 sponds to 673 lm. (This is the new definition; to 10,000lx. The moon has an of prior to 1970 the figure was different). 0.1 lx. Indoor is normally a few 1 The SI unit of solid angle is the steradian [sr] hundred lux. Considering not just the sun, but Luminous efficiency is the ratio of and is defined in a similar way to the radian – the luminance of the sky as a whole ; a clear luminous to radiant flux at a particular the area of a sphere subtended by a cone of noon sky, near the horizon, has a luminance 2 wavelength. Relative luminous efficiency is angle 1sr is equal to the radius squared. In of around 10,000cd/m . A cloudy sky at sunset terms of “full angle” the cone is » 65.54°. is around 10cd/m 2.

BCRA CAVE RADIO & ELECTRONICS GROUP, JOURNAL 27, SEPTEMBER 1997 9 PHOTOMETRICS UPDATED EXTRACT FROM CREG JOURNAL. FILE: FOOT3-UP.DOC REV. 8. LAST SAVED: 01/02/01 15:14 Fluorescent Tube Drivers

A selection of references to circuits for driving fluorescent tubes collected by David Gibson.

Traditionally, most battery-powered and shut-down facilities to help maximise DC-to-DC Converter Transistors, battery life. fluorescent used a one-transistor Zetex AN81 application note, oscillator driving a transformer. It was not June 1992, p517 & Feb. 1993, p165 IGBT Switching Reduces Ballast Size, only inefficient, but the output waveform had [reprint] Oct. 1994, p869 a d.c. bias that caused one end of the tube to The application note AN81 covers the Zetek IGBT types ZCN0545 and darken. But technology has moved on since use of the company’s range of E-line bipolar ZCP0545 are used in an 11W off-line and mosfet transistors in DC-to-DC fluorescent lamp ballast. They are so efficient those days. Electronic ballast is now big converters providing up to 10W for small they can replace TO220/126 bipolar or business – the transistors are fast and equipment such as fluorescent tubes and mosfet transistors and will provide savings in efficient and the coupling Cs (to eliminate flashguns. both cost and circuit volume. the d.c. bias) are of a high quality. Zetek, a Fluorescent Lamp Ballast, Lighting Switches, by Martin Eccles Sept semiconductor firm, now manufacture a IR application note, October 1994, p837 1994, p752 [reviewed in CREGJ 21] range of transistors specifically designed for The IR2151 is a high voltage, high speed, A look at some efficient switching high frequency lamp ballasts. This is one of self-oscillating driver for power mosfets and designs for applications ranging from many cases where it could pay to re-visit an IGBTs. [also brief mention, April 1995, emergency beacons to LCD back-lighting. “old” problem in the light of “new” p349] Modern high-performance chip designs make technology. A quick search of my index to it possible to drive a fluorescent lamp using a Fluorescent Backlighting, transistor with tiny footprint. Electronics World reveals the following LT Application, Dec. 1993, p1037 recent articles. For EW back-issues telephone The circuit using an LT1172 drives two CREG 0181-652 3614 cold cathode fluorescent back-lighting lamps at 92% efficiency. It also features dimming

Foot-candles: Photometric Units – continued from page 9 Relationship between Relationship between the nit for cd/m2. Other names exist for sub- Luminance and Luminous intensity and illumination multiples of basic units; for example the Emittance The area subtended by a cone of solid , which is 100mlx (i.e. 1 lm/cm2) and the Both these quantities describe the angle W is r2W so a source of intensity I cd , which is 100mcd/m2 (i.e. 1cd/cm2). radiated energy from a surface, and it is to be causes an illumination of I/r2 lux at a These units are non-preferred. There are also expected that there is a relationship between distance r. the ‘candle’ units which, confusingly, refer to them. For a Lambert surface it can be shown Example: An LED has an on-axis illumination, and not to luminance A foot- that the relationship is intensity of 3cd and it is shone onto a surface candle is a lumen per square foot, whilst a Luminous emittance [lm/m 2] = 2m away. The illumination at the centre of metre-candle is simply a lumen per square p ´ Luminance [cd/m 2] the beam will therefore be 0.75 lx. The metre, or lux. If the surface is perfectly reflective, as surface is perfectly diffuse, and has a The relationship between luminous well as being perfectly diffuse then the reflectance of 10% so the resulting intensity and luminance mentioned above has emitted flux must equal the incident flux, and luminance will be 24mcd/m2. lead another series of units. A Lambert is 1/p this gives the relationship between cd/cm2, thus a surface with an illumination of illumination and luminance: Units of Measurement 1lm/cm2 (1 phot if you must) has a Luminance [cd/m 2] = Historically the candle (forerunner to the luminance of one Lambert. This unit is large 1/p ´ Illumination [lm/m 2] candela) was defined, not surprisingly, as the and so the milli-Lambert (mL) at 3.183cd/m2 ´ Reflectivity [%] brightness of a candle. Equally unsurprising is more commonly used. Luminance can be a difficult quantity to is the fact that this is a difficult standard to There is also the foot-Lambert, which is get to grips with. For example, it is the maintain. The SI definition of the candela is 1/p cd/ft2, and the metre-Lambert or , luminance of a surface that is significant in repeatable, but difficult to set up in practice. which is 1/p cd/m2. The apostilb is thus the discussions of cameras, lenses and the human It is derived from the luminance of a black luminance of a perfectly diffuse and perfectly eye. A scene luminance in cd/m2 gives rise, body surface at the temperature of freezing radiating surface with an illumination of 1 lx. on the other side of the lens, to an platinum (now accepted to be 2045.5K), at The is a milli-apostilb. This rapidly gets illumination in lux. This is why, for example, standard pressure; the luminance of which is very confusing! that the photopic and scotopic curves are defined to be 60cd/m2 in the normal There are also the Troland, and Luxon, defined for a particular scene luminance and direction. The lumen, which is in some which are the illumination on the retina from not in terms of illumination or luminous respects a more ‘basic’ unit, is derived in a scene of luminance 1cd/m2 when viewed emittance. terms of the candela. through a pupil of aperture 1mm. Some of the SI units described above CREG have been given non-standard names, such as

10 BCRA CAVE RADIO & ELECTRONICS GROUP, JOURNAL 27, SEPTEMBER 1997