Document:

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                                                                  Exhibit 4.7(b)

THE SECURITIES REPRESENTED BY THIS WARRANT HAVE NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS. THE
SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE OFFERED FOR SALE,
SOLD, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION
STATEMENT FOR THE SECURITIES UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
APPLICABLE STATE SECURITIES LAWS, OR AN OPINION OF COUNSEL IN FORM, SUBSTANCE
AND SCOPE REASONABLY ACCEPTABLE TO THE ISSUER THAT REGISTRATION IS NOT REQUIRED
UNDER SAID ACT OR APPLICABLE STATE SECURITIES LAWS OR UNLESS SOLD PURSUANT TO
RULE 144 UNDER SAID ACT. ANY SUCH OFFER, SALE, ASSIGNMENT OR TRANSFER MUST ALSO
COMPLY WITH THE APPLICABLE STATE SECURITIES LAWS.

                          ALLIANCE MEDICAL CORPORATION

                             STOCK PURCHASE WARRANT

Date of Issuance: July 27, 1998                         Number of Shares 150,000

                  For value received, Alliance Medical Corporation, a Delaware
corporation (the "Company"), hereby grants to Russmir Capital Inc., or its
registered assigns (the "Registered Holder"), the right to purchase from the
Company a number of shares of the Company's common stock (the "Common Stock") at
a price per share equal to $2.25 (the "Exercise Price").

                  This Warrant is subject to the following provisions:

                  Section 1. Exercise of Warrant.

                  1A. Exercise Period. The Registered Holder may exercise, in
whole or in part, the purchase rights represented by this Warrant at any time
and from time to time after the Date of Issuance until the fifth anniversary of
the date hereof (the "Exercise Period").

                  1B. Exercise Procedure.

                  (i) This Warrant shall be deemed to have been exercised when
the Company has received all of the following items (the "Exercise Time"):

                  (a) a completed Exercise Agreement, as described in Section 1C
         below, executed by the Person exercising all or part of the purchase
         rights represented by this Warrant (the "Purchaser");

                  (b) this Warrant;

                  (c) if this Warrant is not registered in the name of the
         Purchaser, an Assignment or Assignments in the form set forth in
         Exhibit II hereto evidencing the assignment of this Warrant to the
         Purchaser; and
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                  (d) a check payable to the Company in an amount equal to the
         product of the Exercise Price multiplied by the number of shares of
         Common Stock being purchased upon such exercise (the "Aggregate
         Exercise Price").

                  (ii) A certificate for shares of Common Stock purchased upon
exercise of this Warrant shall be delivered by the Company to the Purchaser
within ten business days after the date of the Exercise Time. Unless this
Warrant has expired or all of the purchase rights represented hereby have been
exercised, the Company shall prepare a new Warrant, substantially identical
hereto, representing the rights formerly represented by this Warrant which have
not expired or been exercised and shall, within such ten-day period, deliver
such new Warrant to the Person designated for delivery in the Exercise
Agreement.

                  (iii) The Common Stock issuable upon the exercise of this
Warrant shall be deemed to have been issued to the Purchaser at the Exercise
Time, and the Purchaser shall be deemed for all purposes to have become the
record holder of such Common Stock at the Exercise Time.

                  (iv) The issuance of certificates for shares of Common Stock
upon exercise of this Warrant shall be made without charge to the Registered
Holder or the Purchaser for any issuance tax in respect thereof or other cost
incurred by the Company in connection with such exercise and the related
issuance of shares of Common Stock. Each share of Common Stock issuable upon
exercise of this Warrant shall, upon payment of the Exercise Price therefor, be
fully paid and nonassessable and free from all liens and charges with respect to
the issuance thereof.

                  (v) The Company shall not close its books against the transfer
of this Warrant or of any share of Common Stock issued or issuable upon the
exercise of this Warrant in any manner which interferes with the timely exercise
of this Warrant, except as required in order to comply with applicable federal
and state securities laws. The Company shall from time to time take all such
action as may be necessary to assure that the par value per share of the
unissued Common Stock acquirable upon exercise of this Warrant is at all times
equal to or less than the Exercise Price then in effect.

                  (vi) The Company shall assist and cooperate with any
Registered Holder or Purchaser required to make any governmental filings or
obtain any governmental approvals prior to or in connection with any exercise of
this Warrant (including, without limitation, making any filings required to be
made by the Company), except that this subsection (vi) will not require the
Company to register the sale of the Common Stock underlying this Warrant under
any federal or state securities laws.

                  (vii) Notwithstanding any other provision hereof, if an
exercise of any portion of this Warrant is to be made in connection with a
registered public offering or the sale of the Company, the exercise of any
portion of this Warrant may, at the election of the holder hereof, be
conditioned upon the consummation of the public offering or sale of the Company
in which case such exercise shall not be deemed to be effective until the
consummation of such transaction.

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                  (viii) The Company shall at all times reserve and keep
available out of its authorized but unissued shares of Common Stock solely for
the purpose of issuance upon the exercise of the Warrants, such number of shares
of Common Stock issuable upon the exercise of all outstanding Warrants. All
shares of Common Stock which are so issuable shall, when issued, be duly and
validly issued, fully paid and nonassessable and free from all taxes, liens and
charges. The Company shall take all such actions as may be necessary to assure
that all such shares of Common Stock may be so issued without violation of any
applicable law or governmental regulation or any requirements of any domestic
securities exchange upon which shares of Common Stock may be listed (except for
official notice of issuance which shall be immediately delivered by the Company
upon each such issuance). The Company shall not take any action which would
cause the number of authorized but unissued shares of Common Stock to be less
than the number of such shares required to be reserved hereunder for issuance
upon exercise of the Warrant.

                  (ix) If the shares of Common Stock issuable by reason of
exercise of this Warrant are convertible into or exchangeable for any other
stock or securities of the Company, the Company shall, at the exercising
holder's option and upon surrender of this Warrant by such holder as provided
above together with any notice, statement or payment required to effect such
conversion or exchange of Common Stock, deliver to such holder (or as otherwise
specified by such holder) a certificate or certificates representing the stock
or securities into which the shares of Common Stock issuable by reason of such
conversion are convertible or exchangeable, registered in such name or names and
in such denomination or denominations as such holder has specified.

                  1C. Exercise Agreement. Upon any exercise of this Warrant, the
Exercise Agreement shall be substantially in the form set forth in Exhibit I
hereto, except that if the shares of Common Stock are not to be issued in the
name of the Person in whose name this Warrant is registered, the Exercise
Agreement shall also state the name of the Person to whom the certificates for
the shares of Common Stock are to be issued, and if the number of shares of
Common Stock to be issued does not include all the shares of Common Stock
purchasable hereunder, it shall also state the name of the Person to whom a new
Warrant for the unexercised portion of the rights hereunder is to be delivered.
Such Exercise Agreement shall be dated the actual date of execution thereof.

                  Section 2. Subdivision or Reorganization.

                  2A. Subdivision or Combination of Common Stock. If the Company
at any time subdivides (by any stock split, stock dividend, recapitalization or
otherwise) one or more classes of its outstanding shares of Common Stock into a
greater number of shares, the Exercise Price in effect immediately prior to such
subdivision shall be proportionately reduced (but not below its par value) and
the number of shares of Common Stock obtainable upon exercise of this Warrant
shall be proportionately increased. If the Company at any time combines (by
reverse stock split or otherwise) one or more classes of its outstanding shares
of Common Stock into a smaller number of shares, the Exercise Price in effect
immediately prior to such combination shall be proportionately increased and the
number of shares of Common Stock obtainable upon exercise of this Warrant shall
be proportionately decreased.

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                  2B. Reorganization, Reclassification, Consolidation, Merger,
or Sale. Any recapitalization, reorganization, reclassification, consolidation,
merger, sale of all or substantially all of the Company's assets, or other
transaction, which in each case is effected in such a way that the holders of
Common Stock are entitled to receive (either directly or upon subsequent
liquidation) stock, securities, or assets with respect to or in exchange for
Common Stock is referred to herein as an "Organic Change." Prior to the
consummation of any Organic Change, the Company shall make appropriate provision
(in form and substance satisfactory to the Registered Holders of the Warrants
representing a majority of the Common Stock obtainable upon exercise of all
Warrants then outstanding) to insure that each of the Registered Holders of the
Warrants shall thereafter have the right to acquire and receive, in lieu of or
addition to (as the case may be) the shares of Common Stock immediately
theretofore acquirable and receivable upon the exercise of such holder's
Warrant, such shares of stock, securities or assets as may be issued or payable
with respect to or in exchange for the number of shares of Common Stock
immediately theretofore acquirable and receivable upon exercise of such holder's
Warrant had such Organic Change not taken place. In any such case, the Company
shall make appropriate provision (in form and substance satisfactory to the
Registered Holders of the Warrants representing a majority of the Common Stock
obtainable upon exercise of all Warrants then outstanding) with respect to such
holders' rights and interests to insure that the provisions of this Section 2
shall thereafter be applicable to the Warrants (including, in the case of any
such consolidation, merger or sale in which the successor entity or purchasing
entity is other than the Company, an immediate adjustment of the Exercise Price
to the value for the Common Stock reflected by the terms of such consolidation,
merger or sale, and a corresponding immediate adjustment in the number of shares
of Common Stock acquirable and receivable upon exercise of the Warrants). The
Company shall not effect any such consolidation, merger or sale, unless prior to
the consummation thereof, the successor entity (if other than the Company)
resulting from consolidation or merger or the entity purchasing such assets
assumes by written instrument (in form and substance satisfactory to the
Registered Holders of Warrants representing a majority of the Common Stock
obtainable upon exercise of all of the Warrants then outstanding), the
obligation to deliver to each such holder such shares of stock, securities, or
assets as, in accordance with the foregoing provisions, such holder may be
entitled to acquire.

                  2C. Notices.

                  (i) The Company shall give written notice to the Registered
Holder at least 20 days prior to the date on which the Company closes its books
or takes a record (A) with respect to any pro rata subscription offer to holders
of Common Stock or (B) for determining rights to vote with respect to any
Organic Change, dissolution, or liquidation.

                  (ii) The Company shall also give written notice to the
Registered Holders at least 20 days prior to the date on which any Organic
Change, dissolution, or liquidation shall take place.

                  Section 3. Definitions. The following terms have meanings set
forth below:

                  "Common Stock" means the Company's Common Stock, par value
$0.001 per share and any capital stock of any class of the Company hereafter
authorized which is not limited to a fixed sum or percentage of par or stated
value in respect to the rights of the holders thereof

                                      -4-
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to participate in dividends or in the distribution of assets upon any
liquidation, dissolution or winding up of the Company.

                  "Convertible Securities" means any stock or securities
(directly or indirectly) convertible into or exchangeable for Common Stock.

                  "Person" means an individual, a partnership, a joint venture,
a corporation, a limited liability company, a trust, an unincorporated
organization and a government or any department or agency thereof.

                  Section 4. No Voting Rights; Limitations of Liability. This
Warrant shall not entitle the holder hereof to any voting rights or other rights
as a stockholder of the Company. No provision hereof, in the absence of
affirmative action by the Registered Holder to purchase Common Stock, and no
enumeration herein of the rights or privileges of the Registered Holder shall
give rise to any liability of such holder for the Exercise Price of Common Stock
acquirable by exercise hereof or as a stockholder of the Company.

                  Section 5. Warrant Transferable. Subject to the transfer
conditions referred to in the legend endorsed hereon, this Warrant and all
rights hereunder are transferable, in whole or in part, without charge to the
Registered Holder, upon surrender of this Warrant with a properly executed
Assignment (in the form of Exhibit II hereto) at the principal office of the
Company, subject to compliance with applicable federal and state securities
laws.

                  Section 6. Warrant Exchangeable for Different Denominations.
This Warrant is exchangeable, upon the surrender hereof by the Registered Holder
at the principal office of the Company, for new Warrants of like tenor
representing in the aggregate the purchase rights hereunder, and each of such
new Warrants shall represent such portion of such rights as is designated by the
Registered Holder at the time of such surrender; provided that, as long as any
shares subject to the Warrant remain outstanding, this Warrant shall only be
exchangeable in connection with the exchange of the certificate representing
such shares subject to this Warrant pursuant to the Company's Certificate of
Incorporation. The date the Company initially issues this Warrant shall be
deemed to be the "Date of Issuance" hereof regardless of the number of times new
certificates representing the unexpired and unexercised rights formerly
represented by this Warrant shall be issued. All Warrants representing portions
of the rights hereunder are referred to herein as the "Warrants."

                  Section 7. Replacement. Upon receipt of evidence reasonably
satisfactory to the Company (an affidavit of the Registered Holder shall be
satisfactory) of the ownership and the loss, theft, destruction or mutilation of
any certificate evidencing this Warrant, and in the case of any such loss, theft
or destruction, upon receipt of indemnity reasonably satisfactory to the Company
(provided that if the holder is a financial institution or other institutional
investor its own agreement shall be satisfactory), or, in the case of any such
mutilation upon surrender of such certificate, the Company shall (at its
expense) execute and deliver in lieu of such certificate a new certificate of
like kind representing the same rights represented by such lost, stolen,
destroyed or mutilated certificate and dated the date of such lost, stolen,
destroyed or mutilated certificate.

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                  Section 8. Notices. Except as otherwise expressly provided
herein, all notices referred to in this Warrant shall be in writing and shall be
delivered personally, sent by reputable overnight courier service (charges
prepaid) or sent by registered or certified mail, return receipt requested,
postage prepaid and shall be deemed to have been given when received (if hand
delivered) or five days after delivered, sent or deposited in the U.S. Mail or
by overnight courier (i) to the Company, at its principal executive offices and
(ii) to the Registered Holder of this Warrant, at such holder's address as it
appears in the records of the Company (unless otherwise indicated by any such
holder).

                  Section 9. Amendment and Waiver. Except as otherwise provided
herein, the provisions of the Warrants may be amended and the Company may take
any action herein prohibited, or omit to perform any act herein required to be
performed by it, only if the Company has obtained the written consent of the
Registered Holders of Warrants representing a majority of the shares of Common
Stock obtainable upon exercise of the Warrants; provided that no such action may
change the Exercise Price of the Warrants or the number of shares or class of
stock obtainable upon exercise of each Warrant without the written consent of
Registered Holders beneficially owning a majority of the shares subject to the
Warrants.

Section 10. Descriptive Headings; Governing Law. The descriptive headings of the
several Sections and paragraphs of this Warrant are inserted for convenience
only and do not constitute a part of this Warrant. The laws of the State of
Delaware shall govern this Warrant without giving effect to any choice of law or
conflict of law provision or rule.

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                  IN WITNESS WHEREOF, the Company has caused this Warrant to be
signed and attested by its duly authorized officers under its corporate seal and
to be dated the Date of Issuance hereof.

                                          ALLIANCE MEDICAL CORPORATION

                                          By: _______________________________

                                          Name: _____________________________

                                          Its: ______________________________

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                                                                       EXHIBIT I

                               EXERCISE AGREEMENT

To:                                         Dated:

                  The undersigned, pursuant to the provisions set forth in the
attached Warrant, hereby agrees to subscribe for the purchase of ______ shares
of the Common Stock covered by such Warrant and makes payment herewith in full
therefor at the price per share provided by such Warrant.

                                         Signature ____________________

                                         Address ______________________

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                                                                      EXHIBIT II

                                   ASSIGNMENT

                  FOR VALUE RECEIVED, _____________________________ hereby
sells, assigns and transfers all of the rights of the undersigned under the
attached Warrant with respect to the number of shares of the Common Stock
covered thereby set forth below, unto:

Names of Assignee                     Address                     No. of Shares

Dated:                                     Signature    _______________________

                                                        _______________________

                                           Witness      _______________________

                                      -9-<PAGE>   1
                                                                     Exhibit 4.8

NEITHER THIS WARRANT NOR ANY SECURITIES WHICH MAY BE ISSUED UPON CONVERSION
HEREOF HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
"SECURITIES ACT"), APPLICABLE STATE SECURITIES LAWS, OR APPLICABLE LAWS OF ANY
FOREIGN JURISDICTION. THIS WARRANT AND SUCH SECURITIES HAVE BEEN ACQUIRED FOR
INVESTMENT AND NOT WITH A VIEW TO DISTRIBUTION OR RESALE, AND MAY NOT BE SOLD,
OFFERED, PLEDGED, HYPOTHECATED, RENOUNCED OR OTHERWISE TRANSFERRED IN THE
ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT AND ANY
APPLICABLE STATE SECURITIES LAWS AND IN THE ABSENCE OF COMPLIANCE WITH
APPLICABLE LAWS OF ANY FOREIGN JURISDICTION, OR AN OPINION OF COUNSEL
SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED AND SUCH
FOREIGN JURISDICTION LAWS HAVE BEEN SATISFIED.

--------------------------------------------------------------------------------

Warrant No. W-__                                                    July 6, 2000

                                     Warrant

                  Alliance Medical Corporation, a Delaware corporation (the
"Company"), for value received, hereby certifies that _______________, or its
registered assigns (the "Registered Holder"), is entitled, subject to the terms
set forth below, to purchase from the Company, shares of the Company's Series B
Preferred Stock, with a par value of $.001 (the "Warrant Stock") to be issued in
the Company's Next Equity Financing (as defined in the Convertible Promissory
Note of even date herewith), at an exercise price per share equal to the initial
liquidation value of the Warrant Stock ("Purchase Price"). This Warrant may be
exercised at any time after the closing of the Next Equity Financing and on or
before the Expiration Date (as defined in Section 6 below). The Warrant Stock
purchasable upon exercise of this Warrant and the Purchase Price per share shall
be adjusted from time to time pursuant to the provisions of this Warrant.

                  This Warrant is issued pursuant to, and is subject to the
terms and conditions of, a Convertible Note and Warrant Purchase Agreement dated
as of the date hereof ("Original Issue Date") among the Company and certain
investors named therein (the "Purchase Agreement") pursuant to which certain
convertible promissory notes in an aggregate principal amount of Five Hundred
Thousand Dollars ($500,000) (collectively, the "Notes") and certain warrants
(including this Warrant) were issued.
<PAGE>   2
                  1.       Number of Shares. Subject to the terms and conditions
                           hereinafter set forth, the Registered Holder is
                           entitled, upon surrender of this Warrant, to purchase
                           from the Company a number of shares of Warrant Stock
                           (subject to adjustment as provided herein) equal to
                           (a) the original principal amount of the Registered
                           Holder's Note multiplied by ten percent (10%),
                           divided by (b) the Purchase Price (as of the date
                           hereof).

                  2.       Exercise.

                  (a) Manner of Exercise. Subject to the last sentence of this
Section 2(a), this Warrant may be exercised by the Registered Holder, in whole
or in part, by surrendering this Warrant, with the purchase form attached hereto
as Exhibit A duly executed by such Registered Holder or by such Registered
Holder's duly authorized attorney, at the principal office of the Company, or at
such other office or agency as the Company may designate, accompanied by payment
in full of the Purchase Price payable in respect of the number of shares of
Warrant Stock purchased upon such exercise. The Purchase Price may be paid by
cash, check, wire transfer, or by the surrender of promissory notes or other
instruments representing indebtedness of the Company to the Registered Holder,
or pursuant to a net exercise as provided in Section 2(c) below.

                  (b) Effective Time of Exercise. Each exercise of this Warrant
shall be deemed to have been effected immediately prior to the close of business
on the day on which this Warrant shall have been surrendered to the Company as
provided in Section 2(a) above. At such time, the person or persons in whose
name or names any certificates for Warrant Stock shall be issuable upon such
exercise as provided in Section 2(d) below shall be deemed to have become the
holder or holders of record of the Warrant Stock represented by such
certificates.

                  (c) Net Issue Exercise.

                            (i) In lieu of exercising this Warrant in the manner
provided above in Section 2(a), the Registered Holder may elect to receive
shares equal to the value of this Warrant (or the portion thereof being
canceled) by surrender of this Warrant at the principal office of the Company
together with notice of such election in which event the Company shall issue to
such Registered Holder a number of shares of Warrant Stock computed using the
following formula:

                  X =    Y (A - B)
                         ---------
                              A

Where             X =    The number of shares of Warrant Stock to be issued to
                         the Registered Holder pursuant to this net exercise

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                  Y =    The number of shares of Warrant Stock purchasable
                         under this Warrant (at the date of such calculation).

                  A =    The fair market value of one share of Warrant Stock (at
                         the date of such calculation).

                  B =    The Purchase Price (adjusted to the date of such
                         calculation).

                            (ii) For purposes of this Section 2(c), the fair
market value of each share of Warrant Stock (or, each share of Common Stock, to
the extent all shares of Preferred Stock of the Company have been converted into
shares of the Company's Common Stock) on the date of calculation shall mean with
respect to each share of Warrant Stock:

                                 (A) if the exercise is in connection with an
initial public offering of the Company's Common Stock, and if the Company's
Registration Statement relating to such public offering has been declared
effective by the Securities and Exchange Commission, then the fair market value
per share shall be equal to the initial "Price to Public" of the Company's
Common Stock specified in the final prospectus with respect to the offering;

                                 (B) if this Warrant is exercised after, and not
in connection with, the Company's initial public offering, and if the Company's
Common Stock is traded on a securities exchange or The Nasdaq Stock Market or
actively traded over-the-counter:

                                        (1) if the Company's Common Stock is
traded on a securities exchange or The Nasdaq Stock Market, the fair market
value per share shall be deemed to be the average of the closing prices over the
thirty (30) business day period ending three business days before the date of
calculation; or

                                        (2) if the Company's Common Stock is
actively traded over-the-counter, the fair market value per share shall be
deemed to be the average of the closing bid or sales price (whichever is
applicable) over the thirty (30) business day period ending three business days
before the date of calculation; or

                                 (C) if neither (A) nor (B) is applicable, the
fair market value per share shall be the highest price per share which the
Company could obtain on the date of calculation from a willing buyer (not a
current employee or director) for shares of Warrant Stock sold by the Company,
from authorized but unissued shares, as agreed by the Company and the holders of
at least 66-2/3% of the Equity Securities issuable upon exercise of outstanding
warrants purchased pursuant to the Purchase Agreement, unless the Company is at
such time subject to an acquisition as described in Section 6(b) below, in which
case the fair market value of the Warrant Stock shall be deemed to be the value
received by the holders of such stock pursuant to such acquisition.

                                       3
<PAGE>   4
                  (d) Delivery to Holder. As soon as practicable after the
exercise of this Warrant in whole or in part, and in any event within ten (10)
days thereafter, the Company at its expense will cause to be issued in the name
of, and delivered to, the Registered Holder, or as such Registered Holder (upon
payment by such Registered Holder of any applicable transfer taxes) may direct:

                           (i) a certificate or certificates for the number of
shares of Warrant Stock (or Common Stock) to which such Registered Holder shall
be entitled, and

                           (ii) in case such exercise is in part only, a new
warrant or warrants (dated the date hereof) of like tenor, calling in the
aggregate on the face or faces thereof for the number of shares of Warrant Stock
equal (without giving effect to any adjustment therein) to the number of such
shares called for on the face of this Warrant minus the number of such shares
purchased by the Registered Holder upon such exercise as provided in Section
2(a) or 2(c) above.

                  3.  Adjustments.

                  (a) Redemption or Conversion of Equity Securities. At the
election of holders of 66 2/3% in interest of the Warrant Stock issuable upon
exercise of all warrants issued pursuant to the Purchase Agreement (assuming
exercise in full of this Warrant and all other warrants issued pursuant to the
Purchase Agreement), this Warrant shall automatically become exercisable for
that number of shares of Warrant Stock equal to the number of shares of Warrant
Stock that would have been received if this Warrant had been exercised in full.

                  (b) Stock Splits and Dividends. If outstanding shares of the
Company's Equity Securities shall be subdivided into a greater number of shares
or a dividend in Equity Securities shall be paid in respect of Equity
Securities, the Purchase Price in effect immediately prior to such subdivision
or at the record date of such dividend shall simultaneously with the
effectiveness of such subdivision or immediately after the record date of such
dividend be proportionately reduced. If outstanding shares of Equity Securities
shall be combined into a smaller number of shares, the Purchase Price in effect
immediately prior to such combination shall, simultaneously with the
effectiveness of such combination, be proportionately increased. When any
adjustment is required to be made in the Purchase Price, the number of shares of
Warrant Stock purchasable upon the exercise of this Warrant shall be changed to
the number determined by dividing (i) an amount equal to the number of shares
issuable upon the exercise of this Warrant immediately prior to such adjustment,
multiplied by the Purchase Price in effect immediately prior to such adjustment,
by (ii) the Purchase Price in effect immediately after such adjustment.

                  (c) Reclassification, Etc. In case there occurs any
reclassification or change in the outstanding securities of the Company or of
any reorganization of the Company (or any other corporation the stock or
securities of which are at the time receivable upon the exercise of this
Warrant) or any similar corporate reorganization on or after the date hereof,
then and in each such case the Registered Holder, upon the exercise hereof at
any time after the consummation of such reclassification,

                                       4
<PAGE>   5
change, or reorganization, shall be entitled to receive, in lieu of the stock or
other securities and property receivable upon the exercise hereof prior to such
consummation, the stock or other securities or property to which such Registered
Holder would have been entitled upon such consummation if such Registered Holder
had exercised this Warrant immediately prior thereto, all subject to further
adjustment pursuant to the provisions of this Section 3.

                   (d) Adjustment Certificate. When any adjustment is required
to be made in the Warrant Stock or the Purchase Price pursuant to this Section
3, the Company shall promptly mail to the Registered Holder a certificate
setting forth (i) a brief statement of the facts requiring such adjustment, (ii)
the Purchase Price after such adjustment and (iii) the kind and amount of stock
or other securities or property into which this Warrant shall be exercisable
after such adjustment.

                  (e) Conversion of Preferred Stock. Immediately prior to the
closing of any public offering of the Company's Equity Securities in which the
Company's outstanding Preferred Stock is automatically converted into shares of
Common Stock, any portion of this Warrant not then exercised will thereafter be
exercisable for the number of shares of the Company's Common Stock that would
have resulted from the conversion, pursuant to the Company's Certificate of
Incorporation in effect on that date, of the maximum number of shares of
Preferred Stock that could have been acquired by the Holder upon the exercise of
the unexpired portion of this Warrant immediately prior to such public offering.

                  4.  Transfers.

                  (a) Unregistered Security. Each Registered Holder of this
Warrant acknowledges that this Warrant and the Warrant Stock of the Company have
not been registered under the Securities Act of 1933, as amended (the
"Securities Act"), and agrees not to sell, pledge, distribute, offer for sale,
transfer or otherwise dispose of this Warrant or any Warrant Stock issued upon
its exercise in the absence of (i) an effective registration statement under the
Act as to this Warrant or such Warrant Stock and registration or qualification
of this Warrant or such Warrant Stock under any applicable U.S. federal or state
securities law then in effect, or (ii) an opinion of counsel, satisfactory to
the Company, that such registration and qualification are not required. Each
certificate or other instrument for Warrant Stock issued upon the exercise of
this Warrant shall bear a legend substantially to the foregoing effect.

                  (b) Transferability. Subject to the provisions of Section 4(a)
hereof, this Warrant and all rights hereunder are transferable, in whole or in
part, upon surrender of the Warrant with the properly executed assignment (in
the form of Exhibit B hereto) at the principal office of the Company; provided,
however, that no such transfer shall be made without the consent of the Company
which consent shall not be unreasonably withheld; provided, further, that this
Warrant may not be transferred in part unless the transferee acquires the right
to purchase all of the Registered Holder's shares of Warrant Stock hereunder,
unless such transfer is made to affiliates, partners or family members of such
Registered Holders.

                                       5
<PAGE>   6
                  (c) Warrant Register. The Company will maintain a register
containing the names and addresses of the Registered Holders of this Warrant.
Until any transfer of this Warrant is made in the warrant register, the Company
may treat the Registered Holder of this Warrant as the absolute owner hereof for
all purposes; provided, however, that if this Warrant is properly assigned in
blank, the Company may (but shall not be required to) treat the bearer hereof as
the absolute owner hereof for all purposes, notwithstanding any notice to the
contrary. Any Registered Holder may change such Registered Holder's address as
shown on the warrant register by written notice to the Company requesting such
change.

                  5. No Impairment. The Company will not, by amendment of its
charter or through reorganization, consolidation, merger, dissolution, sale of
assets or any other voluntary action, avoid or seek to avoid the observance or
performance of any of the terms of this Warrant, but will (subject to Section 14
below) at all times in good faith assist in the carrying out of all such terms
and in the taking of all such action as may be necessary or appropriate in order
to protect the rights of the Registered Holder of this Warrant against
impairment.

                  6. Termination. This Warrant (and the right, if any, to
purchase securities upon exercise hereof) shall terminate upon the earlier to
occur of the following (the "Expiration Date"): (a) the sale, conveyance,
disposal, or encumbrance of all or substantially all of the Company's property
or business or the Company's merger with or into or consolidation with any other
corporation (other than a wholly-owned subsidiary corporation) or any other
transaction or series of related transactions in which more than fifty percent
(50%) of the voting power of the Company is disposed of, provided that this
Section 6 shall not apply to a merger effected exclusively for the purpose of
changing the domicile of the Company, and (b) five (5) years after the closing
of the initial public offering of the Company's Common Stock pursuant to a
registration statement under the Securities Act.

                  7.  Notices of Certain Transactions.  In case:

                  (a) the Company shall take a record of the holders of its
Equity Securities (or other stock or securities at the time deliverable upon the
exercise of this Warrant) for the purpose of entitling or enabling them to
receive any dividend or other distribution, or to receive any right to subscribe
for or purchase any shares of stock of any class or any other securities, or to
receive any other right, to subscribe for or purchase any shares of stock of any
class or any other securities, or to receive any other right, or

                  (b) of any capital reorganization of the Company, any
reclassification of the capital stock of the Company, any consolidation or
merger of the Company with or into another corporation (other than a
consolidation or merger in which the Company is the surviving entity), or any
transfer of all or substantially all of the assets of the Company, or

                  (c) of the voluntary or involuntary dissolution, liquidation
or winding-up of the Company, or

                                       6
<PAGE>   7
                  (d) of any redemption of the Equity Securities or mandatory
conversion of the Equity Securities into Common Stock of the Company, then, and
in each such case, the Company will mail or cause to be mailed to the Registered
Holder of this Warrant a notice specifying, as the case may be, (i) the date on
which a record is to be taken for the purpose of such dividend, distribution or
right, and stating the amount and character of such dividend, distribution or
right, or (ii) the effective date on which such reorganization,
reclassification, consolidation, merger, transfer, dissolution, liquidation,
winding-up, redemption or conversion is to take place, and the time, if any is
to be fixed, as of which the holders of record of Equity Securities (or such
other stock or securities at the time deliverable upon such reorganization,
reclassification, consolidation, merger, transfer, dissolution, liquidation,
winding-up, redemption or conversion) are to be determined. Such notice shall be
mailed at least ten (10) days prior to the record date or effective date for the
event specified in such notice or such earlier date as notice is given to or
approval is sought from shareholders generally.

                  8. Reservation of Stock. The Company will at all times reserve
and keep available, solely for the issuance and delivery upon the exercise of
this Warrant, such shares of Warrant Stock and other stock, securities and
property, as from time to time shall be issuable upon the exercise of this
Warrant.

                  9. Exchange of Warrants. Upon the surrender by the Registered
Holder of any Warrant or Warrants, properly endorsed, to the Company at the
principal office of the Company, the Company will, subject to the provisions of
Section 4 hereof, issue and deliver to or upon the order of such Registered
Holder, at the Company's expense, a new Warrant or Warrants of like tenor, in
the name of such Registered Holder or as such Registered Holder (upon payment by
such Registered Holder of any applicable transfer taxes) may direct, calling in
the aggregate on the face or faces thereof for the number of shares of Equity
Securities called for on the face or faces of the Warrant or Warrants so
surrendered.

                  10. Replacement of Warrants. Upon receipt of evidence
reasonably satisfactory to the Company of the loss, theft, destruction or
mutilation of this Warrant and (in the case of loss, theft or destruction) upon
delivery of an indemnity agreement (with surety if reasonably required) in an
amount reasonably satisfactory to the Company, or (in the case of mutilation)
upon surrender and cancellation of this Warrant, the Company will issue, in lieu
thereof, a new Warrant of like tenor.

                  11. Mailing of Notices. Any notice required or permitted
pursuant to this Warrant shall be in writing and shall be deemed sufficient upon
receipt, when delivered personally or sent by courier, overnight delivery
service or confirmed facsimile, or forty-eight (48) hours after being deposited
in the regular mail, as certified or registered mail (airmail if sent
internationally), with postage prepaid, addressed (a) if to the Registered
Holder, to the address of the Registered Holder most recently furnished in
writing to the Company and (b) if to the Company, to the address set forth below
or subsequently modified by written notice to the Registered Holder.

                  12.  No Rights as Shareholder.  Until the exercise of this
Warrant, the Registered Holder of this Warrant shall not have or exercise any
rights by virtue hereof as a shareholder of the Company.

                                       7
<PAGE>   8
                  13. No Fractional Shares. No fractional shares of Equity
Securities will be issued in connection with any exercise hereunder. In lieu of
any fractional shares which would otherwise be issuable, the Company shall pay
cash equal to the product of such fraction multiplied by the fair market value
of one share of Warrant Stock on the date of exercise, as determined in
accordance with Section 2(c) above.

                  14. Amendment or Waiver. Any term of this Warrant may be
amended or waived upon written consent of the Company and the holders of at
least 66-2/3% of the Warrant Stock issuable upon exercise of outstanding
warrants purchased pursuant to the Purchase Agreement. By acceptance hereof, the
Registered Holder acknowledges that in the event the required consent is
obtained, any term of this Warrant may be amended or waived with or without the
consent of the Registered Holder, provided, however, that any amendment hereof
that would materially adversely affect the Registered Holder in a manner
different from the holders of the remaining warrants issued pursuant to the
Purchase Agreement shall also require the consent of Registered Holder.

                  15. Headings.  The headings in this Warrant are for purposes
of reference only and shall not limit or otherwise affect the meaning of any
provision of this Warrant.

                  16. Governing Law.  This Warrant shall be governed, construed
and interpreted in accordance with the laws of the State of Arizona without
giving effect to principles of conflicts of law.

                                      ALLIANCE MEDICAL CORPORATION

                                      _____________________________
                                      By:

                                      Its:

                                       8
<PAGE>   9
                                    EXHIBIT A
                                  PURCHASE FORM

To:__________________________         Dated:

                  The undersigned, pursuant to the provisions set forth in the
attached Warrant No. ______, hereby irrevocably elects to purchase ______ shares
of the Warrant Stock covered by such Warrant and herewith makes payment of
$__________, representing the full purchase price for such shares at the price
per share provided for in such Warrant.

                  The undersigned acknowledges that it has reviewed the
representations and warranties contained in Section 3 of the Purchase Agreement
(as defined in the Warrant) and by its signature below hereby makes such
representations and warranties to the Company. Defined terms contained in such
representations and warranties shall have the meanings assigned to them in the
Purchase Agreement, provided that the term "Purchaser" shall refer to the
undersigned and the term "Securities" shall refer to the Warrant Stock.

                  The undersigned further acknowledges that it has reviewed the
market standoff provisions set forth in Section 5 of the Stockholders Agreement
dated as of July 19, 1999 among the Company and certain holders of the Company's
securities and agrees to be bound by such provisions.

                                Signature:_________________________________

                                Name (print):______________________________

                                Title (if applic.)_________________________

                                Company (if applic.)_______________________
<PAGE>   10
                                    EXHIBIT B
                                 ASSIGNMENT FORM

                  FOR VALUE RECEIVED, ___________________________ hereby sells,
assigns and transfers all of the rights of the undersigned under the attached
Warrant with respect to the number of shares of Equity Securities covered
thereby set forth below, unto:

       Name of Assignee          Address/Facsimile Number         No. of Shares

Dated:______________________             Signature:__________________________

                                                   __________________________

                                         Witness:____________________________

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