<PAGE>   1
                                                                Exhibit 10.10(f)

                            SUPPLEMENTAL TERMS LETTER



As of January 3, 1997

International Remote Imaging Systems, Inc.
9162 Eton Avenue
Chatsworth, CA 91311

Attention:    Martin S. McDermut, Vice President, Finance &
              Administration & CFO

         RE:  AMENDED AND RESTATED PROMISSORY NOTE DATED JANUARY 3, 1997, IN
              THE ORIGINAL PRINCIPAL SUM OF $4,900,000.00 ("NOTE") EXECUTED
              BY INTERNATIONAL REMOTE IMAGING SYSTEMS, INC., A DELAWARE
              CORPORATION ("BORROWER") IN FAVOR OF CITY NATIONAL BANK, A
              NATIONAL BANKING ASSOCIATION ("CNB")

Dear Mr. McDermut:

         This is to confirm that CNB will extend the credit facility more
completely described in the enclosed Note, subject to the additional terms and
conditions set forth herein. Capitalized terms not defined in this letter have
the meanings given them in the Note. This letter is hereby incorporated into the
Note (this letter and the Note, collectively, the "Note").

                        A. ADDITIONAL EVENTS OF DEFAULT.

         The following shall constitute additional Events of Default under the
         Note:

1.       Any obligee of Subordinated Debt shall fail to comply with the
         subordination provisions of the documents or instruments, including,
         without limitation, any subordination agreement, evidencing or relating
         to such Subordinated Debt;

2.       Failure of Borrower to furnish CNB, within the times specified, the
         following statements:

         2.1      Within forty-five (45) days after the end of each monthly
                  accounting period of each fiscal year, a financial statement
                  consisting of not less than a balance sheet and income
                  statement, prepared in accordance with generally accepted
                  accounting principles consistently applied, which financial
                  statement may be internally prepared;


<PAGE>   2


Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 2



         2.2      Within sixty (60) days after the end of each quarterly
                  accounting period of each fiscal year, a financial statement
                  consisting of not less than a Form 10-Q.;

         2.3      Within ninety (90) days after the close of each fiscal year, a
                  copy of the annual report, on Form 10-K for such year for
                  Borrower and the Subsidiaries; and

         2.4      Such additional information, reports and/or statements as CNB
                  may, from time to time, reasonably request;

3.       Failure of Borrower to maintain the following:

                  3.1      Tangible Net Worth plus Subordinated Debt of not less
                           than the following amounts as of the stated effective
                           date;

<TABLE>
<CAPTION>
                                    Effective Date             Minimum Amount
                                    --------------             ----------------
<S>                                                            <C>  
                                        3/31/97                $  (1,300,000.00)
                                        6/30/97                $  (1,000,000.00)
                                        9/30/97                $    (750,000.00)
                                       12/31/97                $     (50,000.00)
                                        3/31/98                $     550,000.00
</TABLE>

                  3.2      A ratio of Total Senior Liabilities to Tangible Net
                           Worth plus Subordinated Debt of not more than 21.50
                           to 1 as of March 31, 1998;

                  3.3      A ratio of Current Assets to Current Liabilities of
                           not less than the following amounts as of the stated
                           effective date; and

<TABLE>
<CAPTION>
                                       Effective Date              Minimum Ratio
                                       --------------              -------------
<S>                                                                <C>
                                          3/31/97                    0.76 to 1
                                          6/30/97                    0.76 to 1
                                          9/30/97                    0.77 to 1
                                         12/31/97                    0.83 to 1
                                          3/31/98                    0.87 to 1
</TABLE>

<PAGE>   3


Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 3


                  3.4      A ratio of Cash Flow from Operations to Debt Service,
                           cumulative from the beginning of each calendar year,
                           of not less than the following amounts as of the
                           stated effective date.

<TABLE>
<CAPTION>
                                       Effective Date               Minimum Ratio
                                       --------------               -------------
<S>                                                                 <C>
                                           3/31/97                    0.60 to 1
                                           6/30/97                    0.90 to 1
                                           9/30/97                    1.00 to 1
                                          12/31/97                    1.25 to 1
                                           3/31/98                    1.25 to 1"
</TABLE>

4. Failure of Borrower within five (5) days after execution and delivery of this
letter to grant CNB a duly perfected security interest, with the exception of
the existing TOA lien, in all patents, copyrights and trademarks held by
borrower.

                                 B. DEFINITIONS.

         For purposes of the Note, the following terms have the following
meanings:

         "CASH FLOW FROM OPERATIONS" shall be determined on a consolidated basis
for Borrower and the Subsidiaries and shall mean the sum of (a) net income after
taxes earned, plus (b) amortization of intangible assets, plus (c) interest
expense, plus (d) depreciation expensed, plus (e) any other non-cash charges, in
each case, as adjusted for (f) change in deferred taxes.

         "CURRENT ASSETS" shall be determined on a consolidated basis for
Borrower and the Subsidiaries in accordance with generally accepted accounting
principles consistently applied, including deposits and securities held by CNB
as collateral, but excluding, however, from the determination of Current Assets,
loans to shareholders, management or employees, amounts due from Subsidiaries or
affiliates, deferred costs, and other intangible assets.

         "CURRENT LIABILITIES" shall be determined on a consolidated basis for
Borrower and the Subsidiaries in accordance with generally accepted accounting
principles consistently applied, and shall include without limitation (a) all
principal and accrued interest payments on Subordinated Debt required to be made
within one (1) year after the date on which the determination is made; and (b)
all indebtedness payable to stockholders, affiliates, Subsidiaries or officers
regardless of maturity, unless such indebtedness shall have been subordinated to
CNB, on terms satisfactory to CNB.


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Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 4




         "DEBT SERVICE" shall mean (a) the $1,200,000.00 annual principal
payments under this note, prorated per the appropriate period, plus (b) all
interest incurred on borrowed money during the twelve month period ending on the
date of determination.

         "SUBORDINATED DEBT" shall mean indebtedness of Borrower or any
Subsidiary, the repayment of principal and interest of which is subordinated to
CNB, on terms satisfactory to CNB (including, without limitation, the
indebtedness owing to Digital Imaging Technologies, Inc. ("DITI") evidenced by
that certain Seven Million & 00/100 Dollars ($7,000,000.00), eight and one half
percent (8.50%) Subordinated Note due 2001, dated July 29, 1996 by Borrower in
favor if DITI.

         "SUBSIDIARY" shall mean any corporation, the majority of whose voting
shares are at any time owned, directly or indirectly by Borrower and/or by one
or more Subsidiaries.

         "TANGIBLE NET WORTH" shall mean the total of all assets appearing on a
balance sheet prepared in accordance with generally accepted accounting
principles consistently applied for Borrower and the Subsidiaries on a
consolidated basis, minus (a) all intangible assets, including, without
limitation, unamortized debt discount, affiliate, employee and officer
receivables or advances, goodwill, research and development costs, patents,
trademarks, the excess of purchase price over underlying values of acquired
companies, any covenants not to compete, deferred charges, copyrights,
franchises and appraisal surplus; minus (b) all obligations which are required
by generally accepted accounting principles consistently applied to be reflected
as a liability on the consolidated balance sheet of Borrower and the
Subsidiaries; minus, (c) the amount, if any, at which shares of stock of a
non-wholly owned Subsidiary appear on the asset side of Borrower's consolidated
balance sheet, as determined in accordance with generally accepted accounting
principles consistently applied; minus (d) minority interests; and minus (e)
deferred income and reserves not otherwise reflected as a liability on the
consolidated balance sheet of Borrower and the Subsidiaries.

         "TOTAL SENIOR LIABILITIES" shall mean, as of any date of determination,
the amount of all obligations that should be reflected as a liability on a
consolidated balance sheet of Borrower and the Subsidiaries prepared in
accordance with generally accepted accounting principles consistently applied,
less Subordinated Debt.



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Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 5



                       C. ADDITIONAL TERMS AND CONDITIONS.

         The following additional terms and conditions shall also apply to the
Note:

         1. FEES. Borrower shall pay to CNB a non-refundable modification fee
for the following Legal Expenses of $15,000.00; Appraisal Fee/ABL Audit Fee of
$7,290.00; Documentation Fee/ABL Valuation Service Fee of $1,500.00 and Loan Fee
of $25,000.00, plus reimbursement of all expenses associated with completion of
this modification and costs associated with the perfection of the lien on
intangible assets, plus outside legal counsel agreed to by Borrower of
approximately $5,000.00, due and payable in full upon execution of this letter
and the Note.

         2. SUBORDINATION OF DEBT. All obligations of Borrower to Digital
Imaging Technologies, Inc., a Delaware corporation shall be subordinated in
right of repayment to all obligations of Borrower to CNB, as evidenced by and
subject to the terms and provisions of draft eight and one half percent (8.50%)
Senior Subordinated Note due 2001 provided under cover of letter dated July 15,
1996.

         3. ENVIRONMENTAL INDEMNIFICATION. Due to the environmentally sensitive
nature of the industry in which Borrower is principally engaged and upon which
CNB will rely as its primary source of repayment, and in consideration of CNB
extending credit to Borrower, Borrower has agreed to indemnify CNB against any
claims that may arise as a result of Borrower's business activities that are
environmental in nature and for which CNB may be named as a liable party.

         Borrower agrees that it shall indemnify and hold harmless CNB, its
parent company, subsidiaries and all of their respective directors, officers,
employees, agents, successors, attorneys, and assigns from and against any loss,
damage, cost, expense, or liability directly of indirectly arising out of or
attributable to the use, generation, manufacture, production, storage, release,
threatened release, discharge, disposal, or presence of a hazardous substance
on, under, or about Borrower's property or operations or property leased to
Borrower, including but not limited to attorneys' fees (including the reasonable
estimate of the allocated cost of in-house counsel and staff). For these
purposes, the term "hazardous substances" means any substance which is or
becomes designated as "hazardous" or "toxic" under any Federal, state, or local
law. This indemnity shall survive repayment of Borrower's obligations to CNB.

         Except for documents and instruments specifically referenced herein or
in the Note, this letter and the Note constitute the entire agreement of the
parties hereto and


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Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 6


supersedes any prior or contemporaneous oral or written agreements,
understandings, representations, warranties and negotiations, if any, which are
merged into this letter and the Note. If you agree to accept the terms of this
letter and the Note, please sign the


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Martin S. McDermut, VP, Finance & Administration, CFO
International Remote Imaging Systems, Inc.
As of January 3, 1997
Page 7


enclosed acknowledgement copy of this letter, as well as the enclosed Note, and
return them to me on or before April 15, 1997.


Sincerely,

CITY NATIONAL BANK, a national
banking association



By: /s/ Charles Solomon
    ----------------------------------------------
    Charles Solomon, Senior Vice President/Manager



By: /s/ Bruce E. Corey
    ----------------------------------------------
    Bruce E. Corey, Vice President


Accepted and Agreed this 9th day of April, 1997.


INTERNATIONAL REMOTE IMAGING SYSTEMS, INC.,
a Delaware corporation



By: /s/ Martin S. McDermut
    ---------------------------------------------
    Martin S. McDermut, Vice President
    Finance and Administration/CFO