MXPA00000222A - Measurement of hot container wall thickness - Google Patents

Abstract

A method and apparatus of measuring wall thickness of hollow glass articles (12), such as molded glass containers having interior and exterior wall surfaces, includes the steps of measuring intensity of radiation emitted by the article at a first wavelength (at 18) at which intensity varies as a function of both temperature at the surfaces and wall thickness between the surfaces, and at a second wavelength (at 24) at which intensity varies as a function of temperature at the surface substantially independent of wall thickness between the surfaces. Since the first intensity measurement is a function of both wall thickness and temperature, while the second intensity measurement is a function solely of surface temperature, wall thickness between the surfaces can determined (at 26) as a combined function of the first and second intensity measurements.

Description

METHOD TO MEASURE THE THICKNESS OF THE WALLS OF A HOT CONTAINER FIELD OF THE INVENTION The present invention is directed to the measurement of the thickness of glass articles such as empty glass containers, and very particularly to a method and apparatus for measuring the thickness of molded glass articles as a function of visible radiation. and / or infrared emitted by the articles while they are still hot from the training process.

BACKGROUND OF THE INVENTION A number of techniques have been proposed, including radio frequency, capacity measurement measurement techniques and optics, to measure the thickness of the wall of vacuum-molded glass containers after the vessels have cooled for example , in the so-called cold end of the manufacturing process, however, it is desirable to obtain the measurement of the thickness of the wall as soon as possible in the REF: 32433 manufacturing process, although any corrective action that may be necessary may be implemented as fast as possible, therefore reduce the manufacture of unsatisfactory items. It is therefore desirable to provide a technique for measuring the wall thickness of molded glass containers and other similar articles as soon as possible following the molding process. Up to now it has been recognized that glass containers that are still hot from the molding process emit radiation in the infrared range, and that this radiation can be measured in an effort to determine the characteristics of the thickness of the wall. For example, US Patents Nos. 2,915,638 and 3,356,212 propose to measure the infrared energy radiation of the outer surface of the hot containers, and to use the resulting data to derive the thickness information from the container wall. Once the containers have cooled down, the thick parts of the containers will retain more heat than the thin parts, and the temperature of the outer surface will therefore be higher in the thicker portions of the container. The thickness information of the wall can therefore be deduced from the temperature profiles of the containers. However, the above proposal does not show a technique for obtaining an absolute measure of the thickness of the container wall at the extreme end of the manufacturing process, and this is a general objective of the present invention to provide such a technique.

A method of measuring the wall thickness of empty glass articles, such as molded glass containers having interior and exterior wall surfaces, according to the present invention, includes the steps of measuring the intensity of the electromagnetic radiation emitted by an article at a first wavelength at which the intensity varies as a function of both temperatures on the surfaces and the thickness of the walls between the surfaces, and at a second wavelength at which the intensity varies as a function of the surface temperature at the surface of the article substantially independent of the thickness of the wall between the surfaces. Where the first intensity measurement is a function of both the thickness of the wall and the temperature, while the second measure of intensity is a function of temperature only, the thickness of the wall between the surfaces can be determined as a combined function of the first and second intensity measurements. (It would be appropriate, of course, that the term "wavelength" would normally enclose a range of 1 wave ongit because the registers do not respond only to a specific wavelength.) In some preferred embodiments of the invention, the first and the second measure of intensity are obtained from the radiation emitted from a point on the surface of the article. A relationship between the thickness of the wall and the temperature of the surface at this point on the surface of the article is developed from these intensity measurements. The intensity of the radiation emitted from other points on the surface of the article can be measured at the wavelength at which the intensity varies only as a function of the surface temperature, and the thickness of the wall can be determined as other points on the surface of the article such as a combined function of said intensity measurements and the relationship between the thickness of the wall and the temperature of the previously developed surface. In some preferred embodiments of the invention, the recorders include an apparatus, area recorder having a number of sensitive elements and means for focusing on such elements of light energy (visible and / or infrared) emitted from different points on the surface of the container , and a second recorder responds to the energy emitted from a particular point on the surface of the container. An absolute measure of the thickness of the vessel wall is obtained from the output of the second recorder by responding to the energy emitted from the particular point of the surface at the first wavelength, and from the output of the element in the focused area recorder. at the same point and responding to the energy emitted at the second wavelength. Given this absolute measure of the thickness of the wall, and due to the relationship between the thickness of the wall and the surface temperature at this point on the surface of the container, the thickness of the wall at other points on the surface of the container may be determined as a function of the energy indicative of the temperature of the external surface incident on the other elements of the area recorder. In other preferred embodiments of the invention, a reflector is placed between the two infrared recorders and the container or other article under inspection such that the detectors have inspection fields that are coincident on the surface of the container. In this way, the sensors simultaneously receive radiation from a particular point or area on the surface of the vessel to develop the associated signals representative of the intensities in the first and second wavelengths. The reflector is coupled to a motor or other suitable mechanism to move the reflector in such a way that the matching inspection fields of the detectors effectively sweep the surface of the container. In this way, the outputs of the detectors can be searched in increments of the detector movement to obtain the comparative signal data to determine the thickness of the walls in sequential positions along the surface of the container. More preferably, in this embodiment of the invention, the reflector is moved and the detector output is recorded in increments of movement of the container such as to obtain thickness data along the entire surface of the container. When inspecting containers that are hot from the molding process, the inspection can be improved while the containers are moved along the linear conveyor between the machine in which the molding is improved and the annealing furnace by placing an inspection system optical on both sides of the conveyor to obtain thickness data from both sides of the container. The first wavelength at which the intensity is measured as a function of both temperatures on the surface of the container, and the thickness of the wall between the surfaces, is a wavelength at which the wall of the article or container is substantially transparent. The second wavelength at which the intensity is measured as a function of the temperature at the surface, and independent of the thickness of the wall between the surfaces, is a wavelength at which the wall of the article or container is substantially opaque Transparency and opacity are, of course, relative terms. The composition of the glass of a wall of the container is substantially transparent to the energy according to the present invention when the maximum wall thickness is at least 5%. The wall of the container is substantially opaque to the energy according to the present invention when the wall t ransmittance to the infrared energy is less than 1%. In the preferred implementation of the invention the indicative of the energy of both, glass temperature and wall thickness is in the visible and infrared range of 0.4 to 1.1 microns. The energy in which the wall is substantially opaque, and at which intensity therefore varies as a function of the surface temperature and substantially independent of the thickness of the wall, is preferably in the infrared range of 4.8 to 5.0 microns, and more preferably to about 5.0 microns. Those with response characteristics within these ranges can be obtained from available commercial standard registers.

BRIEF DESCRIPTION OF THE FIGURES.

The invention, together with the additional objects, features and advantages thereof, will be better understood from the following description. The appended claims and the accompanying drawings in which: Figure 1 is a schematic diagram of a basic embodiment of the present invention; Figure 2 is a schematic diagram of a modification of the embodiment of Figure 1; Figure 3 is a schematic diagram of one embodiment of the invention for measuring the thickness of the wall around the entire outer surface of an empty glass container; Figure 4 is a schematic diagram of an apparatus for measuring the thickness of the bottom wall of a container according to the present invention; Figure 5 is a schematic diagram of an apparatus for measuring the thickness of the side wall of a container according to a further embodiment of the invention; Figure 6 is a schematic diagram similar to that of Figure 5 but illustrating yet another embodiment of the invention; and Figures 7A, 7B and 7C are schematic diagrams illustrating the calibration of the embodiment of Figure 2.

DETAILED DESCRIPTION OF THE PREFERRED MODALITIES Figure 1 illustrates an apparatus 10 for measuring the thickness of the wall of an empty glass container 12 according to a basic embodiment of the invention. The radiant energy emitted from a point 14 on the outer surface of the container 12 is directed by lenses 16 to a first recorder 18, and by a divider 20 and lenses 22 to a second recorder 24. The divider 20 can be eliminated if the lenses 22 are positioned to focus towards the recorder 24 the energy emitted from the same point 14 in the container 12 as energy emitted to the recorder 18. That is, both recorders 18, 24 receive the radiated energy substantially from the same point 14 on the surface container 12. The recorders 18, 24 provide the respective electrical output signals to an information processor 26, which directs to a screen 28 to provide wall thickness information to a system operator or user, which it can provide a scrap signal to the suitable means for sorting the container 12 of the manufacturing process. The information screen can also be used to control the training process. The recorder 18, which may include suitable filters, provides its electrical output signal as a function of the radiation intensity at a first wavelength at which the wall of the container 12 is substantially transparent. In this way, the radiation at this incident wavelength in the recorder 18 is radiated from the volume of the glass between the surfaces 12a and 12b of the container 12, also as the volume of the glass between the surfaces 12c and 12d. The amount of energy incident in the recorder 18, and the output signal of the recorder, is a function of both, the temperature of the glass container in the different surfaces of the wall and the sum of the two thicknesses of the container wall ( near and far) - for example, the thickness between the surface 12a, 12b and the thickness between the surfaces 12c and 12d. The conventional glasses used for the manufacture of containers are substantially transparent to the energy in the wavelength range of 0.4 to 1.1 microns, and the wavelengths in this range are preferred for the recorder 18. The recorder 24, which includes once again the appropriate filters are responsible for, and therefore provide an output as a function of, the energy at the second wavelength at which the wall of the container 12 is substantially opaque. That is, the intensity of incident energy in the recorder 24 varies as a function of the temperature on the outer surface of the container 12 at point 14, and substantially independent of the thickness of the wall between the outer and inner surfaces of the container. The conventional glasses used for the manufacture of the containers are their stancialmente opaque to the energy in the range of wavelength of 4.8 to 5.0 microns, and a wavelength of substantially 5.0 microns is preferred to obtain the measurement of surface temperature. Since the output of the recorder 18 varies as a function of both, the temperature on the surface of the wall of the container and the thickness of the wall between the surfaces, while the output of the recorder 24 varies as a function of the temperature in the outer surface of the container and independent substantially of the thickness of the wall between the surfaces, the information processor 26 can determine the thickness of the absolute wall between the surfaces 12a and 12b, and the surfaces 12c, 12d, as a combined function of said measurements of intensity signals. Figure 2 illustrates a modified embodiment 30 of the apparatus illustrated in Figure 1. In this embodiment, the recorders 18, 24 associated with the lenses 16, 22 are arranged on diametrically opposite sides of the container 12. The apparatus 32, such as a pedestal , is coupled ope ration on to the container 12 in the inspection station 30 to rotate the container about its central axis; and providing the signals indicative of increments of the container rotation to the information processor 26 by means of an encoder 34. Alternatively, the container 12 can be rotated at a constant angular velocity, and increments of container rotation can be obtained at equal increments of time. It is important in both embodiments of Figures 1 and 2 that the recorders 18, 24 inspect substantially the same point 14 on the outer surface of the container. In the embodiment of Figure 2, the point 14 is inspected by the recorder 18 through the container. Any deformity in the thickness of the wall will reflect the inspection of the recorder 18 away from the point 14. Similarly, since the intensity of the signal in the recorder 18 varies as a function of two wall thicknesses, it is assumed in each embodiment that these thicknesses of wall are identical. In the embodiment of Figure 2, the container 12 can be rotated on its axis and the thickness measurement of the wall obtained at the desired increments of the rotation of the container. Figures 7A, 7B and 7C illustrate this principle. A recorder 24e (4.8 to 5.0 micron e_s) is disposed on each side of the container 12, and a recorder 18e (0.4 to 1.1 microns) is placed on the left side only. If the signal of the recorder 18e and the signal averages of the recorders 24e are used to determine the double average of the thickness of the wall. The side wall of the glass is cooled proportionally to the thickness of the wall. Therefore, the double average of the thickness of the wall can be converted to the thickness in the left and right walls by using the signals of the recorders 24e in the left and right walls. Once a particular point is calculated, the ratio of the cooled glass is proportional to the thickness that can be used to determine the thickness of the glass for all other points in the vessel using the signals from the recorders 24e (proportional to the temperature only ). The calibration of the particular point should be at a point where the register 18e is known to inspect through the left side of the container the right side at the same point where the right register 24e is inspecting. Figures 7A and 7B illustrate the correct calibration points, while 7C is incorrect. Figures 7A and 7B can be distinguished from Figure 7C by the use of recorders 24e and. find a point where the change in the horizontal and horizontal signal indicate that the thickness on the left side is not changing. Figure 3 m shows a third embodiment 40 according to the present invention for measuring the thickness of the wall completely around the outer surface of the container 12. Four area recording devices 24a, 24b, 24c and 24d are placed in an area rectangular in increments of 90 ° around the outer circumference of the container 12. Each b-area recording device 24a, 2, 24c, 24d has an association with the lenses 22a, 22b, 22c, 22d to focus on the emitted energy emitted from a quadrant cin, reference 1 of container 12, as the apparatuses 24a, 24b, 24c, 24d collectively see the complete circumference of the container. Each area recording device 24a, 24b, 24c, 24d consists of a multiple of CCD recording elements arranged in a rectangular area device NxM, such that each of the recording elements in each apparatus receives the radiated energy from a corresponding or small point. area on the outer surface of the container. The divider 20 is positioned so as to extract a portion of the radiated energy from a specific point 14 the outer surface of the container, and to direct said energy towards a recorder 18. The various elements of the area devices 24a, 24b, 24c, 24d correspond to the energy at a wavelength in which the energy varies only as a function of the temperature of the outer surface and independent of the thickness of the wall - for example, at a preferred wavelength of 5.0 microns - while the recorder 18 is corresponding to the energy at a wavelength such that the intensity varies as a function of both, the temperature at the different surfaces of the container 12 and the thickness of the the wall between the surfaces - for example, in the preferred range of 0.4 to 1.1 microns - the output of the register 18, and the output of the specific recording element in the apparatus 24a that receives the energy from the point 14 of the outer surface of the container, it is employed by the information processor 26 to obtain an absolute measure of the wall thickness at point 14, and likewise to develop a relationship between the thickness of the wall and the temperature of the outer surface. This ratio t ra rat e ra / g rosor at point 14 of the container can then be used in combination with the temperatures of the outer surface of the container developed at all other points around the circumference of the container by the other different elements in the container. the recording devices 24a, 24b, 24c, 24d to determine the thickness of the container wall at each of the other points inspected by the recording devices. Figure 4 shows another modified embodiment 50 of the present invention for measuring the thickness of the bottom 52 of the container 12. The thickness measurement of the bottom of the container can be obtained more real than the thickness of the side wall because only a thickness of the wall in particular it is wrapped. The area recording apparatus 24a cooperates with the lenses 22a to see the entire area of the bottom 52 of the container and independent of the thickness of the bottom. The output of the recorder 18, and the output of the element in the recording apparatus 24a which inspects the point 14a in the bottom 52 of the container, are used to determine the thickness of the absolute wall at the point 14a, and then develop the relationship between the thickness of the wall and the temperature of the surface. This relationship is employed by the information processor 26 (Figure 1) in combination with the output of the other elements in the recording apparatus 24a to determine the thickness of the wall at other points around the bottom of the container. Figure 5 shows a system 53 according to another modified embodiment of the invention. In the system 53, a prism 54 having reflecting surfaces 56, 58 is positioned in such a way that the fields of vision of the detectors 18, 24 through the lenses 16, 22 are coincident in the adjacent surface of the container 12. The The prism of the mirror 54 is mounted on a pivot 60 which is coupled to a motor or other suitable device 62 for rotating the prism of the mirror 56 under the control of the information processor 26. As the prism of the mirror 56 is rotated near the pivot 60 , simultaneously the functions of the prism of the mirror to scan both detectors on the surface of the container 12 while maintaining the matching fields of the inspection. The container 12 is carried by a linear conveyor 64, as conventionally used to transport the containers while they are hot from the forming process of the molding machine of the container to the annealing furnace. The linear movement of the conveyor 64 is recorded at 32a, in the encoder 34 and feeds the information processor. Then, the information processor 26 can control the operation of the mirror prism motor 62 and scan the outputs of the detectors 18, 24 in increments of movement of the container along the conveyor 64 effectively to scan the entire area of the surface opposite of the container as it moves. An identical system 53 may be provided on the opposite side of the conveyor 64 to scan the surface area of the container. Thus, the area of the entire surface of the vessel is scanned as it passes from the molding machine to the annealing furnace, and the information processor 26 can collect and display a complete two-dimensional map of the thickness of the container against the position of both, axially and circumferentially of the container. More than two systems 53 may be employed, such as four systems as in Figure 3. Figure 6 shows a mode 66 which is similar to that of Figure 5, except that the prism of the mirror 54 in Figure 5 is replaced. by a flat baffle or mirror 68 mounted on a pivot 60 controlled by a motor 62. Once again, the mirror 68, which can be flat, concave or of other suitable geometry, functions to reflect the inspection fields of the detectors 18, 24 on the adjacent surface of the container 12 in such a way that the inspection fields coincide on the surface of the container. The mirror 68 is pivoted under the control of the information processor 26 to obtain the thickness data according to the present invention, as previously described. If the glass is very opaque, then the signal in the range of 0.4 to 1.1 microns can not be used to calibrate the signal from 4.8 to 5.0 microns. However, the signal proportional to the temperature of the surface (4.8 to 5.0 icrones) can be calibrated using a different technique. The total amount of glass in a container is constant closely, while the distribution can vary. Therefore, the average wall thickness for the entire container can be constant and known. This can be used to calibrate the signal average of the recorder 24 (4.8 to 5.0 microns). This known thickness average renders unnecessary the particular calibration point of the recorder 18 (0.4 to 1.1 microns). Preferably, a map of the temperature of the surface against the position is obtained for the entire rec ip i e, and then this map is used in conjunction with the average thickness of the known wall to determine the thickness of the wall current around the container.

DECLARATION OF THE BEST METHOD KNOWN TO CARRY OUT THE INVENTION It is noted that in relation to this date, the best method known to the applicant to carry out the aforementioned invention, is that which is clear from the present description of the invention. Having described the invention as above, property is claimed as contained in the following

Claims (23)

1. A method for measuring the thickness between the surfaces of a hot-formed glass article that emits radiation, characterized in that it consists of the steps of: a) measuring a first intensity of such radiation at a first wavelength at which the radiation is emitted from both surfaces of the article, b) the measurement of a second intensity of such radiation at a second wavelength in which the radiation is substantially emitted entirely from only one surface of 1 article, and c) the determined thickness of the article between the surfaces as a combined function of the first and second intensity measurements mentioned in steps (a) and (b) above.

The method set forth in claim 1, characterized in that the mentioned steps (a) and (b) are carried out by: d) providing the first and second detection means for responding to radiation in a first and second wavelength respectively, e) the positioning of the reflective means between said detection means and the article of the form that said detection means have inspection fields that coincide in the article, and f) the movement of the means of detection. reflection mentioned in such a way that the inspection fields mentioned will sweep the article.

The method set forth in claim 2, characterized in that it comprises the additional step of g) the scanning of the first and second detection means mentioned is in increments of movement in the mentioned reflecting means.

The method set forth in claim 3, characterized in that it comprises the additional step of: h) improving said steps (f) and (g) in increments of movement of the article with respect to said reflecting means.

The method set forth in any preceding claim for measuring the wall thickness of the vacuum molded glass articles having an inner and outer wall surface while the articles are hot from the molding process, said method characterized in that it consists of the steps of: (a) measuring a first intensity of the radiation emitted by an article at a first wavelength in which the wall of the article is substantially transparent such that said first intensity varies as a function of both temperatures on the surface of the article and the thickness of the wall between said surfaces. (b) The measurement of a second intensity of the radiation emitted by the article at a second wavelength in which the wall of the article is substantially opaque such that the said second intensity varies as a function of the temperature at the surface of the article and independent of the thickness of the wall between the surfaces, and (c) The determination of the thickness of the wall between the surfaces of the article as a combined function of the said first measure of intensity in said step (a) and said second measure of intensity in said step (b).

The method set forth in claim 5, characterized in that it consists of the additional steps of: (d) the development from said first and second intensity measurements in steps (a) and (b) mentioned as a ratio between the thickness of the wall and the temperature of the surface at a point of the article. (e) measuring the intensity of the radiation emitted from at least one other point of the article at the second mentioned wavelength, and (f) determining the thickness of the wall at at least one other point mentioned in the article as a function combined of the intensity measurement mentioned in said step (e) and the aforementioned relationship developed in the mentioned step _ (d).

The method set forth in claims 6, characterized in that said pri wavelength is in the range of 0. 4 to 1.1 mi c r one s.

The method set forth in claim 7, characterized in that the second second wavelength is in the range of 4.8 to 5.0 microns.

The method set forth in claim 8, characterized in that said second wavelength is substantially 5.0 microns. .

The method set forth in any preceding claim 5-9, characterized in that said steps (a) and (b) are carried out by: (d) providing the first and second detection means for responding to radiation in a first and second wavelength respectively, (e) placing the reflective means between said detection means and the article such that said detection means have inspection fields that coincide in the article, and (g) the movement of the means reflects it is mentioned in such a way that the aforementioned matching inspection fields sweep the article. .

The method set forth in Claim 10, characterized in that it consists of the additional step of: (g) scanning the aforementioned first and second detection means in increments of movement in the said reflective means. .

The method set forth in claim 11, characterized in that it consists of the step a d i c i_p nal of: (h) the relation of the mentioned steps (f) and (g) in increments of the movement of the article with respect to the mentioned reflecting means. .

An apparatus for measuring the thickness of the wall of molded and empty glass articles having interior and exterior wall surfaces while the articles are hot from the molding process, characterized in that: means for measuring the external arrangement of the article at a first intensity of the radiation emitted per article at a first wavelength in which the intensity varies as a function of both, the temperature at the mentioned surfaces and the thickness of the wall between the mentioned surfaces, the means for measuring the external arrangement of the article to a second ^ intensity of the radiation emitted by the article at a second wavelength in which the intensity varies as a function of the aforementioned surface temperature and independent of the wall thickness between the surfaces mentioned, and the means for determining the thickness of the wall between said surfaces as a combined function of the first and second intensities mentioned. .

The apparatus set forth in claim 13, characterized in that it further consists of: means for developing from the first and second mentioned intensities a relationship between the thickness of the wall and the temperature of the surface of the article, the means for measuring the intensities of the radiation emitted from other points on the surface of the article to _ the aforementioned second wavelength, and the means for determining the thickness of the wall at the other points mentioned in the article as a combined function of the mentioned intensities emitted at said other points and related between the mentioned wall thickness and the temperature Of the surface. .

The apparatus set forth in claim 14, characterized in that both mentioned means for measuring the intensities at a second mentioned wavelength consist of an area recording device having a multiple of recording elements and means for focusing said infrared energy emitted from said elements. the different points on the surface of the article. .

The apparatus set forth in claim 15, characterized in that a majority of the area register recorders are positioned so as to inspect different areas of the article surface simultaneously. .

The apparatus set forth in claim 13, characterized in that said first wavelength is in the range of 0.4 to 1.1 microns. .

The apparatus placed in the claim 17, characterized in that said second wavelength is in the range of 4.8 to 5.0 microns. .

The apparatus placed in the claim 18, characterized in that said second wavelength is substantially 5.0 microns. .

The apparatus set forth in claim 13, characterized in that it also contains the means placed between the article and the aforementioned means for measuring said first and second intensities such as said means for measuring the first and second mentioned intensities having inspection fields. which coincide in the article, and the means for moving said placed means such that said coinciding inspection fields sweep the article.

21. The apparatus set forth in claim 20, characterized in that it also contains the means for indicating the scanning data of the energy intensities in said wavelengths in said means for measuring said intensities.

22. The apparatus placed in the claim 21, characterized in that it also contains the means for controlling the movement of said means and the aforementioned scanning means for sweeping the article and scanning said data in increments of the movement of the article.

23. A method for measuring the thickness of the walls of the vacuum molded glass articles having a predetermined average wall thickness, and while the articles are hot from the molding process, characterized by the steps of: (a) the measurement of the intensity of the radiation emitted by the article indicating the temperature of the surface, (b) the determination of the thickness of the wall of the article as a combined function of the intensity measurement in said step (a) and the predetermined range of the thickness of the wall mentioned. . The method of claim 23, characterized in that said step (a) consists in the development of a map of the temperature of the surface against the position around the article, and wherein the step (b) means step Step of determining the thickness of the wall as a combined function of the aforementioned map and the average thickness of the mentioned wall. SUMMARY OF THE INVENTION A method and an apparatus for measuring the thickness of the walls of empty glass articles, such as molded glass containers having inner and outer surfaces, including the steps of measuring the intensity of the radiation emitted by the article to a first length of wave in which the intensity varies .co or a function of both, the temperature at the surface and the thickness of the wall between the surfaces, and at a second wavelength at which the intensity varies as a function of the surface temperature substantially independent of the thickness of the wall between the surfaces. Since the first measure of intensity is a function of both the thickness of the wall and the temperature, while the second measure of intensity is a function only of the surface temperature, the thickness of the wall between the surfaces can be determined as a combined function of the first and second measures of intensity.